The 252 is compatible with all modern (pro bias) Stax headphones, and especially the other Lambdas, because all Lambdas have similar drivers and hence driving needs.
I have heard the 207 and 507, and they're different. The 207 has a nicely balanced frequency spectrum, but sounds a bit polite, while the 507 has somewhat more bass, and a very good, tighter and deeper bass at that, and at the same time it has more treble. Its treble is smooth (it really is) but your ears will still need some adjustment. Talking about adjustment, the 507's adjustable headband works really well if you don't have a very large head.
I can't say anything about the 307 and 407, but a few weeks ago Stax released the new L500 and L700 Lambdas. The first reviews of the L700 are very positive, so this could be something to look into if you're planning a real upgrade.
If you're planning to stay within the Lambda range, even if that will be with the L700, the Stax tube amps are a very good pairing. I had a SRM-T1 myself, which is for the very most part identical to the current 006tS, and there is definitely some synergy in the midrange between a Lambda and a Stax tube amp. So, if it's between the 323 (or the new 353X) and the 006tS, certainly choose the latter for driving Lambdas IMO.
Personally, I would look into a L700 for now while keeping the 252, and then later get the tube amp, all depending on budget of course. Hope this helps.