I've done a bit of HDMI capture using DVD-Recorders, which can give decent results. Never tested any AVRs though, I'm curious how they perform.
, which according to the specs has a full-frame TBC (if set up with extra memory) + the line-TBC function many of the ADV chips have. How it's set up and how well they handle unstable VHS video I don't know. Can't service manual of the onkyo, I see some panasonic chips on images. Both are composite input only (no S-video) though.
You may or may not need a HDMI splitter capable of stripping HDCP copy protection. DVD/HDD recorders often require this, but I don't know if AVRs commonly require HDCP capable equipment on their hdmi outputs. Also make sure you get something that can capture lossless/uncompressed, many of the Gamer HDMI grabbers can only capture directly to compressed h264.
Not sure what elgato device you've been suggested, only new one they sell with analog capability is the Elgato Video capture, which judging by the driver is some standard conexant or empia dongle (has drivers for both). There are cheaper versions of those around, not really ideal for grabbing directly from a VCR though, they don't deal with unstable VHS video very well (despite what the manufacturers like to claim). They need a TBC or DVD-Recorder in the chain to stabilize the video.
Another thing is NTSC tapes, newer PAL decks can usually play back NTSC tapes with PAL60, but it's not well supported by capture devices. No idea whether the AVRs support this.
I suppose since you have the AVRs, you can get an idea about how well they perform dealing with VHS signals (and video standards) by seeing how the output is on a TV (though the TV will de-interlace and scale).