What brand/model is this red dot? And how was/is it mounted? A red dot should not have any eye-relief issues, those only apply to magnified optics.
I had trouble once getting on paper with a sight at 50yrds. Moved it in closer to 25yrds… still not on paper. Moved it to about 7yrds and was FINALLY on paper (barely). Turns out I was waaaaaaay low. Once I got it close at 7rds (accounting for the height over bore) i moved it back to 25, then 50yards for final zero’ing. So my advice here is try getting the paper closer it may be hitting where you aren’t expecting, and your efforts to fix it may be moving it even further away from center.
As far as red dot vs irons… The answer is usually irons first, then get a red dot. Learning how to align the rifle to irons is a necessary and useful skill. Sometimes (more often on pistols than rifles) people end up “hunting” for the dot if they didn’t raise the firearm just right and the dot is just outside the visible area. Having said that, a red dot is almost always “faster” to bring on target and is super forgiving of your head position so shooting from awkward positions is much easier than with irons.
Most folks will run a red dot with flip-up iron sights, just keep the iron sights down until/unless you need it because the red dot failed. The red dot is your primary sighting system and the irons are a backup. Hence Back-Up Iron Sights (BUIS).
Depending on the height of the red dot, you may be able to use the irons (assuming those are zero’ed well) to help zero the red dot. You basically adjust the red dot to it appears to sit “on top” of the front sight post. This only works for co-witness or lower 1/3rd co-witness height mounts. If you have a really high or really low mount that wont work.