As no-one else has responded yet, I'll have a stab...
I haven't used a 5D, but have used APS-C cameras such as 50D and 550D to digiscope. You are correct that the larger the sensor, then the slower the shutter speeds you will get. You can get around this to an extent by concentrating on slow moving/still subjects, raising the ISO and using timer/cable release etc.
There are basically 2 ways to digiscope with an SLR & birding scope.
The first method is to use a standard prime lens (in the 28-60mm range) connected to the camera as normal, then point it through the eyepiece of the scope. Ideally you would want to connect all of this up so that the camera/lens combo becomes one unit. Typically this would likely involve: Scope-eyepiece-adapter-lens-camera. You might also need a step ring to connect the camera lens's filter threads to the adapter. No T-adapter is needed for this set up.
In the case of Swarovski, which you mentioned, there are at least 2 adapters that will connect the camera to scope. The DCA and the UCA. They also do a DCB adapter which is more suited to smaller compact cameras and compact system cameras.
There are good intro videos from Swarovski on Youtube, for all of these adapters.
Swarovski have also recently introduced a new range of modular scopes, and with them there is a new TLS APO adapter, which in simple terms, replaces the camera lens/adapter combo in the train I listed above. It contains a built-in 30mm pancake lens, and is backwards-compatible with the ATM/ATS scopes because it can be fitted over these scopes' eyepieces using special adapter sleeves. You would need a T-adapter between the camera & TLS APO adapter, but I'm sure I've read that for some reason these new adapters are not compatible with full frame cameras.
The other method is to use the TLS 800 adapter, which replaces the eyepiece/camera lens combo. It contains lenses, hence the cost. The train in this situation would be as follows: Scope-TLS800-T-adapter-camera. I have no personal experience of using it, and older reviews have been rather dismissive of it. However, DSLRs have improved in 2 important ways in recent years; ISO performance and live view (for accurate focussing). I think magnification would be lower than with the camera/lens combo, but quality should be better. For some good examples see here:
http://www.flickr.com/photos/jingbar/sets/72157609644017069/
I know that most of this Swaro kit is over your $1500 budget, but the point is that most other scope manufacturers make similar products, so it's worth researching what they have to offer. I would also look into comparing the results with a more conventional camera/long lens combo such as 400mm prime lens, which might also work out cheaper/more versatile in the long run.
Hope some of this helps
Steve
This thread should also be worth a read:
http://www.birdforum.net/showthread.php?t=77754