Hesitation
 

So I have a 1999 Honda Accord Sedan V6 and recently it has started doing something strange that no matter who I take it to can't tell me what the issue is and how to fix it. When I reach 50mph and above and barely press on the gas to maintain my current speed it hesitates like it is not getting enough gas. Now I know my way around cars for the most part and for the life of me can't figure this one out. The issues goes away once I press on the gas and make the car downshift. I would assume it would be fuel system related issue. Clogged fuel filter, air filter, bad gas etc. So I replaced the air filter, car still does the same,I always run premium gas in it no exceptions. I went to honda and they ran a full check on it. They came back with a list of things that could be the issue but they were not for sure. The list was
EGR Valve
EGR Port Clogged
Transmission Fluid needs to be changed
Bad Transmission
Front Axle Bad (I do know I have two busted cx joins and they are clicking when I go around a curve, but they have been doing this for 2 years and I am waiting till they just go out to replace)

Now, my car has 246,000 miles on it
At 210,000 The timing belt/Water Pump/Spark Plugs and transmission(along with aftermarket transmission cooler was replaced on the car) also I took the head of the engine off and cleaned the EGR port entirely, it was pretty nasty.
I inquired about having honda change the fuel filter. THey are telling me that it is not a replaceable fuel filter that it is located inside the fuel injector and they would have to replace the fuel injector and fuel pump to change the filter. I don't see how this is true because, and correct me if I am wrong, most cars have an inline fuel filter made of charcoal that you can replace? What should I do first. It is time to change the transmission fluid, but would that really be the cause of the car hesitating when pressing on the gas to maintain speed. What I am afraid of doing is replacing all this mess and it still not fixing the issue. ON a final note, my car did have a fluctuating idle intermittently prior to this happening, now that has went away for the most part and now I have this issue. PLease help :)

They're right about the fuel filter. There's only a mesh "sock" inside the fuel tank. Not a routine replacement, you just do that if you measure a problem with fuel pressure. And fuel pressure problems would become worse (not better) when you accelerate.

Use regular gas. The idea that higher anti-knock-index is better is a marketing myth (hesitate to call it "premium"). Your car doesn't call for it.

EGR?? Sure that might be. There's threads about cleaning out the EGR passageways in the intake manifold.

Transmission fluid? I'm tempted to say that someone who knows his way around cars could feel the subtle difference between engine & transmission problems. Maybe the torque converter locking & being reluctant to unlock when you barely press the gas pedal?

Check color, smell, cleanliness, & level of transmission fluid on the dipstick. You know to check ATF level when the engine is all warmed up but turned off? That's unlike many other car companies who want the ATF level checked while the engine is idling. Honda ATF only.