Have you been using regular pump gas with ethanol , or only non-ethanol gas?
With ethanol you could have water or a gel (as in jello) accumulate in the bottom of your fuel tank that can restrict your pickup tube/screen. Been there done that.

Regular gas, but I always add Sta-Bil. Non-ethanol fuel is getting harder and harder to find these days.

Pick-up tubes inside the tank can crack over time. I have seen this be the cause of fuel delivery issues. You're able to get enough fuel to prime the system, but the crack reduces the available constant flow because you're sucking air. A practical way to check for a cracked pick-up tube is to fill the tank completely FULL and try it. If it runs smoothly, the fuel level is submerging the cracks in the pick-up tube. Note that the leak could be at the bulkhead seal, so filling the tank won't catch that leak.

Another fuel system test is to check the fuel system vacuum level. Your mechanic should have done this if he's thorough. All engines have a specification for the availability of fuel. If you make the engine work "too hard" to suck fuel from the tank, it won't get enough. What matters is the total inches of vacuum for your system as experienced by the engine's VRO pump. If you use a filter with too fine of a filter material, you can starve fuel, even with a clean filter. If your anti-siphon valve is sticking due to residue on the ball, you can affect fuel flow. The list goes on for what could cause a fuel restriction. BUT...do that vacuum test and find out just how hard the VRO is having to suck for fuel. If your boat's fuel system is within spec once measured with the vacuum gauge, then you have a weak VRO. THIS is what happened to my Stratos with a Vindicator 200 on it. BTW, if the interior of the fuel line is degraded and collapsing, the fuel vacuum test will show a problem.

I'm betting the vacuum test will fail to meet spec for the engine. This will confirm your need to focus on what is wrong with the boat. Change the filter element anyway - it could be the straw breaking the camel's back. Have you pulled the fuel pick-up assembly to inspect it?

I have tried everything I know to do to get the pick-up tube unscrewed from the tank. It ain't happening! That dang cube is screwed into the tank and corroded just enough to make it next to impossible to turn.

The fact that the problem got better after I changed out the anti-siphon valve makes me think that the problem is not a crack in the pick-up tube, but a small clog in there. I'm thinking its gummed up and just needs to work its way loose.

Compressed air down the tube.
May be temporary but will help you diagnose.

His idea works, temporarily as he said. You'll have to remove the anti-siphon valve to blow it out. Don't forget to remove the filler cap so the air you send in can easily escape. You want a lot of volume.

Can you get to the fuel level sender assembly easily? Removing that may give you a peek into the tank to see what it looks like in there (such as a lot of debris or crud in the bottom of the tank). I use an inspection camera with a flexible goose-neck for this. You can also drop a siphon hose in with the fuel sender removed. Get some samples from the bottom of the tank to see what they look like. Clean gas or debris laden? sludge or clean? etc.

Trick on removing the tank pickup fitting: heat the fitting up with a heat gun.

Some tanks have a fine screen on the end of the pickup tube, so do not. If you can't get the pickup tube out, take off the anti-siphon valve and blow compressed air back thru the pickup tube. If your lucky it will blow the sceen off or apart, then put you an inline fuel filter on and you should be good to go. If it ran good on a portable tank, then the problem is from the motor down to the pickup inlet. I guess you have checked the vent already, if not take the cap off and try it.

on my johnson it was the choke vale diaphragm that was bad did the same this it cost me 13$ on amazon .ocom to buy a wool new kit

UPDATE: I went out yesterday to take another run at this. I took the anti-siphon valve off, connected a flexible hose to it and blew air down the tube several times. I could hear bubbling in the tank when I did it similar to what you hear when you blow down a straw in a drink cup. Compressed air would have been better, but that's not what I did. I also took a small diameter tube that I fed down into the cube/pick-up tube and sprayed a few shots of carb cleaner down there to hopefully clear out any build-up. I reconnected everything and gave it a test run.

It will come up on plane and hit top end speed, but then it starts to taper off to about half speed and every few seconds it will catch and momentarily speed up - a lot like if you were to jam your foot on and off the gas pedal in a car. I ran it for about 30 minutes. There were a few 3-4 minute intervals where it would run great at about 3/4 speed without really losing any power. Anytime it did start to die off, squeezing the primer bulb would always make it power right back up.

Overall, the problem is getting better. Its way better than it was before I replaced the anti-siphon valve when it would come up on plane and then cut back to about 5-10 mph and eventually die. My best guess at this point is a clogged pick-up tube that is slowly getting unclogged. Any chance it could be a weak fuel pump too?

Remember, this problem started out of now where one weekend. It had been running perfect, then I went to the fuel dock on Cedar Creek and put about 10 gal's in. It ran great on the way back to my dock (5-10 min boat ride). I put it in the slip, got it back out about an hour later and the problem started the first time I tried to get up on plane.

Fuel filter stopped up!

That's the same thing mine was doing a couple of summers back. I took off the filter shook it out and blew back through it several times, good as new.

When you connected the external tank, you say it ran fine. Please confirm.

WHen you connected the external tank, where along the boat's fuel system did you connect it? At the engine proper?
When you cnnected that external tank, did you happen to bypass an external fuel filter that is located somewhere under the deck at the rear of the boat? These would typically be of an "oil-filter lookng spin-on" nature.

When you switched over to the external tank, did you bypass your boat's primer bulb? If so, that's your culprit - primer bulb valve flapper is restricting fuel flow. Do not use a cheap one from Wally World unless just as a test. A good one that is ethanol-resistant will be $40. Most recommend you buy the Mercury branded one - it will work with any outboard.

Did you read the whole posting? I don`t think so because the 4th reply is about cleaning the filter.

Gary, I did read all of it, but not all of it again today. I've been involved with this one since the beginning as I've had this type issue a couple of times myself, and seen others with similar. Since he brought up the very good point of when it DID run good, I thought it was worth asking to clarify.

There is often a fuel line splice right at the engine cowling. If he tapped in the aux. tank there, then he was using the aux tank hose and primer bulb. I don't think we have questioned the primer bulb before now, but if what I suspect is true, it is worth checking as the likely culprit. My mechanic buddy finds them doing that (restricting flow) as they disintegrate internally.