1. Is the frame too small for me?
2. Or will fitting a longer seat post and stem ease the problem?
3. Will it be a too much of a compromise; am I better off replacing it?
Hi Alyn and welcome to RetroBike
1. As a general rule of thumb you need to measure the stand over height. Take a tape measure from the floor to the top of the crossbar, that measurement needs to be around 2cm less than your inside leg. If it is you can probably make adjustments to get a better fit. If its a lot less you're going to struggle to get it to feel comfortable.
The saddles for and aft position should be lined up so that when you are sat comfortably on the saddle, your leg is parallel with the seat tube. The saddles nose should be just slightly up. Your seat height should also be adjusted so that you have just a slight bend at the knee when the pedal is in its low position. A lot of people have their saddles too low.
2. Assuming the frame is roughly right but you still feel cramped after the adjustments above, you could look at the stem length to make the handlebars further away from where you are sat. Ideally, if the stem is the right length for you, you should be able to sit comfortably and your eye line through the handlebars should obscure the front hub.
3. Try the above, it will give you a very basic fit. There are all sorts of scientific calculations and tools to get a bike to fit correctly but that should get you somewhere near. Then its best to clock up a few miles to get used to it before passing judgement, a road bikes riding position will always feel completely different to your Trek or Dawes