If you want to spend $250 or less and do it yourself, the one component you should upgrade first is the camera to one that does have a line TBC, S-Video output, and stereo sound output - Last I looked those can be had for about $125-$150 on ebay and if they aren't as described, you can return them for a full refund as it's not as described if it says its used and ends up not actually working - even if returns are not accepted.
If you don't want to do it yourself or mess with hardware that may or may not work, I'd match Costco's price to do it using whatever hardware you want as I have basically one of every device for testing purposes and I like the hardware restoration aspect. Would require shipping the tapes and there's some risk there that things could get lost in the mail though. Box stores won't ever give you raw interlaced files as they are quite large and they probably capture using an H264/mp4 hardware encoder so the files are never really that large at any stage (and not properly deinterlaced), probably not too dissimilar to the elgato video capture. PM me if interested. I believe this site also offers transfer services, but I am not sure of the prices, would encourage you to reach out to admins there as well to see if they'll meet your needs.
Vwestlife did a comparison video of some video conversion services and sometime didn't even have the frame rate correct haha.
Worth a watch if you haven't seen:
https://www.youtube.com/watch?v=SSj3RbdhjzA
For what it's worth, in Vwestlife's conversions, I believe he's just doing a DV firewire capture (which doesn't get a lot of love here, but I think is probably better than any of the big box captures you're likely to get and there's never audio/video sync issues as a bonus), or he'll sometimes use a Sony DVD recorder and then rip the MPEG2 files. In both cases, it's an interlaced capture and he deinterlaces later.