Looking for a good small subwoofer...

In this system there is a separate preamp and 40 watt (20/20) EL-34 tube amp currently powering a pair of Kilpsch RP-600M speakers.

Ideally the setup should work like this:
Preamp out (line level) to the sub or subs. 

Stereo line level crossover inside the sub, around, say 100Hz. Lows goes into its internal solid state amplifier, high-pass filtered audio to output jacks which then connect to the tube amp and to the full range speakers.

I'm not sure which of the subs suggested here will accomplish that.

The cost should be around $500 or less so some of the excellent subs suggested here will not fit the bill.
8'or 10" would be more than enough.
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So far these have been suggested:
Thank you all.

 mijostyn: Kef KF92 and KC62

psf4972: KEF KC62

aggregatebuzz: BIC America F12

waytoomuchstuff: Small B&Ws

balooo2: RSL 10 MKII

dbphd: KEF KC62

dwest1023: B&W DB3i

jjss49: rel t5i/x or t7i/x

sunshdw: SVS 3000 Micro

dweller: Polk Audio PSW505

musicaddict: The SVS SB-2000
    
jayctoy: Pioneer, $349
    
tweak1: GoldenEar ForceField 30 - 8" or 40 - 10"
    
fuzztone: SVS micro or KEF KC62

rocray: Rythmik,REL,or SVS

lak: small REL's

grislybutter: Kef, (not a fan of SVS, REL)

hilde45: Rythmik subs

bigshutterbug:  Totem Kin

soix: SVS SB1000 Pro

Here’s one…

https://www.svsound.com/products/sb-1000

What is the budget?

I wouldn’t use the crossover in a budget sub unless sound quality not important.

I’d run the sub full-range using either a line-in (RCA) or speaker wire coming off the main amp’s speaker connection posts. Use the sub’s volume control to blend things and the frequency knob to eliminate higher-frequencies.

You can get away with a single sub in a small room.

Personally, I’d always go with a 12" sub over an 8 or 10 inch.

RELs in my system