Here are a couple of collet options.
Stick an ER collet chuck in a 4 jaw independent chuck and get it running as true as you want. Smaller ones can be bought with a Ø16 parallel shank, you can go up to ER32 with a Ø32 shank. A cheap stop gap as you build up a collection of the real ones using Martin K's method. The disadvantage is that some of these parallel shanks do not have a through hole. They may also require shortening to get them sticking out as little as possible (not too hard to do with an angle grinder if the shank is hardened) if you get a shank larger than the spindle bore.
Buy a backplate and ER front plate to make a collet chuck that replaces the standard chuck when required. This has been done by plenty of lathe owners.
Parting off (or grooving) using a collet in the spindle nose is always easier than something sticking out a long way either in a chuck or collet mounted anywhere other than one in the spindle. It's just the way the mechanics of parting off works. This is a good reason to aim for the real thing.
Martin C