I have an old canon XH A1 camcorder that uses DV tape. I don't want to use tapes anymore but want to put this camcorder to use so I'm thinking of adding an external video recording device and record from the camcorder's HDMI output.

This device would need to use SDXC card and be able to encode HDMI video to some compressed format. It would also need a display, but no need to be 5 inch large or provide zebra pattern.

I don't know what the name of this type of recorder is. I keep finding the wrong devices on the net. Some requires a PC to capture, some are designed to record TV shows with a remote, some comes with a 5 or 7 inch monitor and adds to the cost, and some cost > $1000. I'd buy a new camcorder if I were to spend $1k, even though a $1k camcorder is not as nice as the XH A1, it is far more useful due to the convenience of using SD card.

I'd like to keep the cost under $500. Any suggestions?

Why go through all the trouble of using a 1440x1080 interlaced camera?
For under $400 you can buy a used GX85.

I'm thinking of adding an external video recording device and record from the camcorder's HDMI output.

The xh-a1 doesn't have a hdmi output, I have used the Sony hvr-dr60 which has a build in 60gb harddrive when I had my xh-a1 and I see you can still find them used. Very reliable unit, never had an issue with it. The advantage was that recording was controlled from the camera, disadvantage was it took 13 seconds to start up. You"ll need a 4 to 6pin i.LINK firewire cable to connect that recorder and a 6 to 6 pin firewire cable and a firewire card for your pc to transfer the footage which goes very fast. There are some other recorders available from what I remember but don't recall which type.

For under $400 you can buy a used GX85.

Imagewise the GX85 outperforms the xh-a1 but in terms of functionality the gx85 is a toycamera compared to the xh-a1. Crank 2 with Jason Statham in 2009 was shot on a xh-a1 so it's not like you can't do a higher quality production with it anymore, the camera's main achillesheel is that it needs light, it's not a low light camera but as long as you have controll over the lightconditions it will do just fine depending on your requirements.

I think you're better off waiting until Global Shutter CMOS becomes mainstream. CCDs are a dying dinosaur, Global Shutter CMOS supports 4K and up, but the price for entry is still too prohibitive (NO, I'm not counting the Blackmagic cameras.)

Rather than use an old old tape recorder and splurging on a BMD Video Assist or Atomos Ninja 2, I'd just suggest you buy a secondhand Panasonic G80/GX85/etc or heck even a 1080 camera like a Panasonic GH3 or GH2 still would be preferable.

Or if you really must buy a camcorder instead, a Sony FS100 or F3 is dirt dirt cheap to buy.

Neither the BMD Video Assist or Atomos Ninja 2 will work with the xh-a1 as you need a recorder with a fireWire connection unless there is a way to go from a firewireconnection to HDMI?

The recorder I suggested is still available second hand on ebay and amazon but it's expensive with prices between 500 to 600 dollar, I also just see you want a screen on the recorder, not sure if you will find any that have fireWire connections.