I recognize where you are coming from and the dilemma you are facing. I used a DVStorm and a Matrox in the past and dumped them as well.
First, you talk about HD, which can be about any format in high definition terms. It can be HDV (tape based), AVCHD (card/disk based), P2 (card based), XDCAM EX (SxS based), XDCAM HD (pro disk based), and what else do you have.
Since you are talking about firewire for capture, I assume you are talking about HDV.
Let's get some fuzziness out of the way:
HDMI is a video transfer protocol, firewire is a data transfer protocol. HDMI is widely and incorrectly touted as a good ingest method. Just to get things clear from the outset, HDMI is great for displaying video, it is lousy for ingest. Getting your DATA into the computer is best done by firewire, because you can keep the timecode, metadata, date and timestamp data and exposure data intact. If you use HDMI, you lose all that information. Second HDMI is no better than firewire. Once recorded on whatever media you use, compression has occurred and the data has been irretreivably lost. Uprezzing and adding 0's to the colorspace does not improve the image. Software can do a better job than the cameras logic circuits.
So capture with firewire, but instead of using PR, you may be better off using HDVSplit, a freeware utility that does a much better job than PR and gives you scene detection.
Forget about anything Matrox, it is money down the drain. Only use firewire for capture and check your camcorder settings to output HDV.
Personally, I would suspect the problem is your system and hard drives are not fast enough to capture HD.
SD to DVD capture daterate requirement is about 7 Mbytes per second, which most consumer level computers can JUST handle.
Depending on resolution, framerate, and capture card, HD requires a bare bare minimum of 15 Mb/sec to as much as 300 Mb/sec
Any computer less than a workstation is normally not capable of handling even the bare minimum, unless, you install 2 identical hard drives connected a RAID controller, which will increase the datarate by at least 50-60 % or more depending on your computer and the controller you get, and which hard drives you get. The black Western Digital is the best on the market for this, and quite affordable, as are RAID controllers for them.
You're lucky you could not even attempt to capture HD with what you have because that could very probably have caused your capturing hard drive in to safe slow mode that you can never recover it from, you can only hope to get whatever files off it that you absolutely have to save, and then toss that hard drive on the scrap heap.