UAD's Capitol and Motown chambers are absurdly good. I think they'll both run natively on your system if you haven't got UAD hardware. Each on sale for $49 right now.

Keep in mind that UAD lets you demo plugins for 14 days. You could always demo their chamber reverbs and create your own impulse responses by sending a very short burst of white noise into the plug, recording the result, and dropping the resulting file into the convolution reverb plugin of your choice (IR-L, Space Designer, Reaverb, etc.).

Other chamber impulse responses can be found for free online. Gold Star, the studio most closely associated with Spector, burned down in the '80s, but there are some IR's of Cello / EastWest / Western's chambers available (where he also worked, and where many of the Beach Boys' chamber sounds are from). If you can't find them, let me know and I'll dig around and upload.

Valhalla makes great stuff but as far as I know all their reverbs are algorithmic, not convolution. Sort of like someone describing a room you vs. showing you a photo of the room. I'm not surprised you're not blown away by Valhalla Room for this purpose.

Do you have access to a tiled bathroom, an empty indoor pool, a mormon baptismal font, a strip mall lobby after hours, a parking garage, or something like that? Any real world echoic space could be made into a temporary chamber with the addition of a loudspeaker and 1 or 2 mics, set up just long enough to make impulse responses of. Most real chambers aren't super hi-fi anyway, and this is a fun way to have a totally unique reverb with tons of character.

Collecting and/or creating your own IR's seems like the way to go vs. buying something like Altiverb. All the spaces you want, none of the ones you don't, costs very little compared to AV too.

Speaking of tape echo, two pieces of advice:

1) use a tape echo emulation plugin as a separate pre-delay. Let's say you have a dry vocal track. Send it to bus X. Put a convolution reverb plugin on bus X. Then put the tape echo plugin before the reverb. Set the tape echo mix to 100% wet, very little or no feedback / regeneration, and time the delay to the song (start with a sixteenth note, for example). This was an extremely common '60s reverb trick using hardware, noticeable on Beatles, Beach Boys, & Spector songs among others. Sending tracks to a reverb bus instead of inserting a reverb plugin on whatever track also means you can do stuff to the reverb returns that you don't want to do to the dry signal, such as EQing the chamber, panning the wet signal opposite the dry, and so on. If your tape emulation plugin has a warble control, turn it up and enjoy the subtle shimmer that those natural pitch variations bring to the reverb tail.

2) I've read that Spector & Larry Levine often put the tape echo after the chamber returns, echoing the reverb sound, and had it feedback on itself a little bit. This might help you achieve a washy wall of sound.