I like this prompt, I had considered a similar thread though I'm not sure I have 5 moves I would make. I have a different list, in some ways the opposite of yours. In general I'm less interested in the batting order or even the bullpen hierarchy, these things are fairly fluid and I don't think sequencing hitters or pitchers differently makes much difference. Case in point, the bullpen needed to get 12 outs last night, with Smyly definitely down and possibly Miller and/or Keegan too. Someone's gotta get the outs and blowing a lead in the 6th counts the same as blowing it in the 9th. I'm also less down on Neris, albeit in the way that I don't see a whole lot of clearly superior options in the current pen.
Send down PCA, call up Mastrobuoni or Canario. PCA's bat is not ready to face major league pitching, and the position player group's primary concern is scoring runs consistently. If you want a PR/LHH on the bench bring up Mastro, if you want an OF you can spot start or catch some thunder then bring up Canario. Let PCA show his readiness with the bat in Iowa, which he really has not done for more than a couple games at a time.
Send down Little, call up Roberts. Little is outside Counsell's circle of trust, is walking a disqualifying number of hitters for the run environment, and isn't getting the Ks he has in the minor leagues that might make that temporary trade off worthwhile. With Leiter and Smyly the replacement doesn't need to be LH, I'm open to arguments for others but Roberts has the greatest potential to be a pop up success that pitches important innings through the summer.
Let Amaya catch tonight, then bench him through the weekend. I'm not going to weep if they dump Gomes for Nido, but this is a position that carries more risk than the average bench player shuffling, so I'd rather they make a decisive move like a trade for Diaz rather than grabbing whatever guy *maybe* can wRC+ 75 for a bit. Amaya I have more belief in but I think he's getting worn down by his struggles and the demands of the position. Play him tonight and Gomes tomorrow like you would normally, then let Gomes catch the full weekend slate. There's an off-day Thursday and a day/day/night weekend series so Gomes won't turn to dust. Hopefully that gives Amaya a boost so he can start building confidence with the bat, which may outweigh the benefits of replacing Gomes with a coinflip waiver claim(which you can still do afterwards)
Another I feel less strongly about would be giving Bote a handful of starts to see if you catch fire and give Morel a mental reset, and if Bote forces the issue consider using Morel over Tauchman in a couple matchups(this can also be Canario independent of Morel/Bote).