Your splash chicks are, assuming you don’t end up with partridge or Columbians (this won’t matter as rec white masks all pattern and ground colour):
E/E (self colour), i+/i+ (wildtype, not dom white), Bl/Bl (splash), C/c (heterozygous rec white, not showing) that’s all that matters for this.
Your blues are the same but Bl/bl (Blue)
If you cross two of your splash or blue chicks, the blue locus doesn’t matter, but for rec white you will get C/C, C/c, c/C and c/c. The quarter that are c/c will be white as they are homozygous rec white. If you bred one of these blue or splash cockerels to your rec white parent hens, you will get half C/c and half c/c instead, improving your chances of getting more whites. Any white chicks from either of these crosses will be fine for breeding whites as long as you don’t use the dom white rooster or his white chicks.
The blues/splashes you have, have the rec white allele as their mothers were all likely rec white, it just doesn’t show without another copy.
Your white chicks are white not because of two rec white but one dom white, if you breed these you will pass on dom white (I/I, I/i+, i+/I are all white, and only i+/i+ are non dom white) and you can’t tell if they are homozygous for either white very well. You shouldn’t breed these for pure white, as their white offspring may still be able to produce non white chicks without you knowing if they can until then.
Breeding homozygous rec white with no dom white is the easiest way to guarantee true breeding whites in your chicks, in your case anyway. The best way to do this is by crossing the non white chicks with the rec white parent hens (this is what I meant that confused you I think)
I hope this makes more sense.