You can actually get a new RAAL Adapter just like the TI-1b, but it is based on the new 1995 adapter (using the stand). I would do that since the TI-1b and the new adapter are great (and sound the same). Your SR1a would sound very nice with the BAT,
I demoed the 1995 Immanis and Magna and I had an issue of not being able to work my jobs with them, especially the Immanis. There is so much sound that I found it hard to concentrate on my work. So, I went and repurchased the SR1a again which consistently sounds great, and I can work late at night with them on
My Magnepan MIni I think is a bit better on top than the LRS+ but can be used only in a small space. The Magnepan 3.7 should be like the Mini. I would do a demo of the following,
Diptyque Products - The Music Room
I have sold off a lot of gear and now given away my RAAL CA-1a phones, so I am down to 2 systems and the SR1a. I would suggest you try and get a TI-1b or order a new 1995 adapter. The cost is not much, and the sound is incredible. Almost as good as the VM-1a. I actually preferred the much cheaper Schitt Mjolnir preamp | Schitt Aegir v1 ($500 used) | TI-1b adapter on the Immanis and Magna over the VM-1a. That is how good the adapter is. I prefer the VM-1a on the SR1a but it is close.
I have a second Aegir v1 coming back from Schitt repair next week. If your BAT has dual output, including RCA then you could connect an Aegir v1 to it along with your LRS+ CODA amp. Just turn off the amp not being used (or Standby). For a few hundred dollars you would have killer sound. I can send out the amp to you if you want to test it out.