PC CPU spike preventing transfer completion

I'm trying to transfer the 12/12/12 concert off my Premiere and am having problems. The recording is 34 GB (TiVo's estimate). I start the transfer and it goes at a good clip (average of 60 Mbps), but eventually the speeds drop down to next to nothing (a few Mbps). When I check my PC the reason for this is that the application doing the transfer is sucking up all the CPU time. Basically it's spinning it's wheels which is hindering the download. I've tried multiple programs (TiVo Desktop, Firefox and Chrome) and the best I've been able get is about 20 GB's worth of the recording. Usually it happens somewhere between 8 GB and 16 GB. Sometimes it recovers and the CPU usage drops, but it doesn't full recover and speeds start to decrease more and more each time until I stop the transfer.

Browsers let me pause and resume the download and while pausing stops the high CPU usage, it returns when resuming. I've tried disabling my Antivirus program, which did seem to help a bit, but in the end didn't make a difference. I've transferred large programs in the past, but nothing this large.

It's really annoying see an approximate GB every few minute transfer rate, drop to a GB every few hour transfer rate. I suppose it would eventually finish in a few days, but I don't feel like waiting to see if it does since the speeds keep dropping.

Any ideas on what I can do here? Is there a way to resume downloads off the Premiere (using MPEG-TS) as that would work around the issue.