I'm not sure what your 900MHz hearing device is, but if it has analog inputs you could just get a digital-to-analog converter box and still use your existing device(s). The telecoil/hearing loop people run across this all the time.
I'm not big on Bluetooth myself, and doubt there are any aids supporting it directly, only indirectly via a streamer device.
One possible problem with using an audio (or video) delay is that I think it might be that the delay is not fixed. Depending on the moment it could be a few ms +/- and not sure if a delay will give satisfactory results.
Of course it's great that you are trying new things, and please report back with your findings. I am using Starkey Wi's right now with the SurfLink Mobile and I use other devices to help in certain circumstances. Starkey also has a "Media" device for connection to a TV but I don't have one yet. The "Mobile" has some of the same features as the "Media", but not quite. So I use a i2i wirelsss RF transmitter to send the TV signal to my person, where I have the "Mobile" in hand. This allows me to have my hands on the Mobile remote and stream at the same time. The i2i is a proprietary 2.4Ghz system and the Starkey a 900MHz one.
2003 - Unitron Conversa - lots of features, poor audio quality. Rejected.
2003 - Sonic Natura 2se - have been happy with them, kept.
2012 - Unitron Moxi 6 - had basically same reaction as Conversa. Rejected.
2012 - Sonic Velocity 12 - Good sound quality, good basic no-frills aid. These are my backups! Great price.
2012 - Siemens Motion 701 CIC. Sounded just "OK". Rejected.
2012 - Starkey Wi i110 - Good, kept. (ReSound maybe better?)