Need integrated for Tyler linbrook Signature

For a solid state integrated, I can hightly recommend the NAD M3. It is powerful and in my setup was somewhat analog, definitely not bright. If you feel the need to use tone controls on some recordings it provides those. I never used them on my M3 but some may like that feature. It also has many other customizing features that most other high end integrateds lack. If the look of componentry interests you, it is a beautiful integrated. It's loaded with flexibility and features for various applications. Unlike the other pieces NAD has made (besides possibly the Silverline), in my opinion, this one is high end. There is one available here now.

Might want to try a Portal Panache - use one with Linbrook System 2

I demoed my Jadis OR on the LS's and had no problem getting bass good response. These speakers are definetly tube friendly, provided the amp has high quality trans as does Jadis.
That would Cayin. Ck out their many models. Maybe the new Cayin 100, with 8 KT88 tubes. Abit over 2K but worth looking into. Besides you have a top class speaker, well worth over the asking price (fair value is $15K, Ty sells them for 1/3 the price), so you need a first class amp.
There's not many first class amps in the 2K range.
good luck

How about a BAT integrated.

I am driving mine right now with a VK200 and they sound great. I also have a Levinson No.29 at 50wpc and it works very well with my Linbrook Sigs.

I've mated the same speakers with the McIntosh MA6900, Mac separates, Bel Canto and Cary SS separates, and the orginal Rowland Concentra, and to this day I greatly miss the Rowland - it was a magical combo (I'd think about going back if I wasn't doing multichannel). All that said, a big caveat is that when I had the Rowland I had a much better room, but I still believe it was a very synergistic combination. To this day I have not had better sound than that.

I have a used Coda Ultra that was wonderful with the Linbrook Signatures. Moved on to separates recently, so if your interested let me know. You can go to the Coda Technologies website for more info on this well built and sonically pure integrated. Ty has used Coda with his speakers at previous audio shows so that should tell you he thinks it's a good match.

I have a T+A PA1230 integrated and a T+A SACD 1250 player. Superb!
I also considered the Rowland Concerto as it is highly recommended.

I also have the Signatures and I am using both the Raysonic 128 and the Wadia 302 as sources I have been quite happy with both a Cayin A100T and a Paragon Three/Five pre-amp/amp combo. Both are very responsive to tube changes. I've only had the Cayin for 3 or 4 months but it has been trouble free. It is well built and operates very well with its remote. It also has both Triode and UL on the fly, although IMHO the Triode mode is a little soft and fuzzy in the upper mids - not a draw back if you like your music laid back though, and the amp runs much cooler so I assume you'd have very long tube life. I put mine in triode for casual/background music. It costs a bit more than you mention but sooner or later they will come up for sale.

I think you might find the 3/5 combo in your budget, and it is also a fine set. Down side is no remote and it is only UL, no triode option. But it runs cool. I've had this combo for 2 1/2 years with out problems. FWIW.