Honda Civic Transmission Trouble

'99 Honda Civic EX, not sure of the Engine size, 150,000 miles.
I am the original owner.

We took the car in a couple months a go and asked for a laundry list of needed or suggested repairs. Inlcuded on the list was a Transmission replacement. The theory being that it has been neglected (couldn't refute that) and the way it shifted and accelerated. In fact the mechanic said he wouldn't even want to perform a Trans flush because he didn't think it would survive afterward. Within a couple of months we got some of the repairs done, including a Trans flush (from a different mechanic). Shortly after, what seems like transmission issues have increased or worsened.

Which brings me to my question... I think there is a problem with the transmission, but I'm not sure and I was hoping to get some other ideas before replacing the entire Transmission. Here are the symptoms - takes longer than expected to shift, and occasionally there is a loud clunk when accelerating and shifting into 2nd gear. Also with in a day or two after the transmission flush the transmission seems to be not transferring power to the wheels. When I go to take off from a complete stop, the engine will rev way up but the car barely moves, but will slowly accelerate and within 15 seconds or so will get to 2nd gear at which point it resumes fairly normal operation. At first it happened once, then several days later again, then a couple days after that twice in one day, finally it happened a handful of times in 15 minutes. Each timeit happens it is from a dead stop. Is this a transmission issue? is really seems like it? More importantly, is it a MAJOR issue? When I had the flush done it was at a Cottman Transmission shop and the mechanic said the fluid wasn't bad at all, slightly discolored, but not burnt or anything. Unfortunately, I have really come to NOT trust his opinion. I plan to get a third opinion from a GoodYear garage tomorrow. Any ideas?

Thanks,
John