That's fine and 1/4, 3/16ths are sure better than trying 1/8th. If it's that loose I think the removal won't be too tough. But I will say this, as long as you get some of the top part broken and recessed you don't have to be anal and get every little piece out.
I don't like using epoxy modified grout as it can be tricky for those that don't do this all the time. I do advise using admix with grout for strength and possibly some more flexibility. Maybe Greg knows more about that. It should bridge over any left over
recessed grout left in place. I will say that everything must be free of dirt, and oils, even impregnated floor sealers and polish that could keep the new grout from bonding to any grout left in place, and indeed the tile edges themselves.
I like it very thin so that it runs into and under any voids when first applied. It will tighten up soon enough unless you are actually pouring the grout out of a pitcher.
Depending on humidity and temps you will have plenty of working time. Overthinning does weaken the grout but most seem to error on the side of trying to work it too stiff like maybe wall tile grout which has to have some body to it or you'll never get it in the joints, it will keep running out until it reaches a point that it will hang. Then you've lost that much time to work a large area. Mixing up different batches is not recommended unless you measure carefully. The color changes with thicker or thinner mixes. It may be subtle but even sealer won't fix that. Darker colors are more affected than light ones, so take heed.
If I left anything out, Greg will catch it.