This is a tough one. With an SPL of 88dB a 300B is going to be a problem. You will get 8 to 13w out of most 300B SETs. Let's assume 10w, you will be getting 94.3dB of volume at 10' from the speaker at full power. That is not a lot of headroom.
In a mid-size room (20 x 20 is definitely mid-size) you are going to want a bit more power.
This website will help.
http://myhometheater.homestead.com/splcalculator.html
Consider your setup and speaker placement. I find 85dB to be an excellent reference volume and you want about 15dB in headroom to cover dynamics. Thus, you want to be able to deliver ~100dB in volume.
Assuming your speakers aren't in the corners of the room and are near the wall (2-4' away) and you listen about 10' from the speakers, you will want at least 30-40
There are not many SETs that deliver that kind of power unless they are parallel SETs which tend to be expensive. I import Art Audio and have done a lot of studying of SET amps. The list is not long that will deliver real power.
If you are looking for a little more in terms of PRAT you could try a different tube. That ARC uses a 6550 which is popular because it is inexpensive and gives you more traditional tube dynamics than a KTXX but is not in the same league as a SET.
What you could look for is Push Pull using a different tube type.
I can only think of one 300B Push Pull from KR and it is not in your price range. Opera - Consonance make a 2A3 Push Pull at 30w called the 880A. I believe it should be in your price range. They no longer have a US Distributor and I have been in touch with them regarding representation. If you are interested, let me know and I will press them.