I can get a Firewire to USB converter easily, but will Premiere be able to download from the camera over this Firewire->USB connection? Or does it only look at a genuine Firewire input?
You can try it, but I doubt it would work. Those 1394/USB bridges might work for hard drives (and probably not well, at that), but the AV/C protocol (that is, video control and capture over 1394) is a different animal. You'd probably have to get an ExpressCard adapter that provided 1394 ports--that's assuming the laptop has an ExpressCard slot.
Is it really about time I junked my beloved HV30 and just got something tapeless instead to get around all these issues?
Black Magic to get HDMI into the PC and work that way?
Tapeless is the way going forward--no question. Lots of options based on budget, so that's probably the largest determining factor of what to get. There's no need for a BMD card with HDMI input, though--that would be only if you were going to be capturing live into the edit system. If you're recording to some form of solid-state media, like an SD card, it's just like copying photos from the SD card in your digital camera. You'd simply pop the card out of the cam and into the computer--or sometimes you can connect the camera via USB as if it were a card reader--and transfer the files to your hard drive for editing. Once the files have been created in camera, the damage has been done, so to speak. The HDMI input on a BMD is for taking a signal directly off the camera's imaging sensor and bypassing the internal compression, whatever flavor it may be. That's fine if you're using the camera in a studio setting, or if you have a really, really, really long cable (joking).
In short, with a tapeless camera, you'll be editing directly with the files created by the camera--it's just a file copying process to get them into your computer to edit.
Hope that helps.