Dave, welcome to the forum! Congrats on taking things into your own hands. It's been over 10 years since I worked for a shotcrete company, but I haven't forgotten everything What we did for setting tile and coping and for the grout was make a mix of white cement and marble dust (white) 1:1 - this was also the plaster mix (though for tile resetting, we would use thinset). Is this the same grout mix you will be using? I would grout the tile before patching the plaster. Then I would modify the mix (substitute fine sand for the marble dust, the color will match better - epecially if you can get sand that has the same colors as the discolored plaster [it'll show as patches anyway, but perhaps not so glaringly as using white plaster]). You might want to brush on a bonding agent to the patch areas before applying the new plaster to help it stick (Laticrete is the brand I know of, but there are probably other manufacturers).
I hope this gives you a few ideas on your project. Again, welcome to the forum - if you need any more help, all you have to do is ask and the nice folks here will do all they can to asist you. - Waste
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