Fields and Qualls both pitched around 50 IP last year. I expect the new guys and Qualls and Fields and Sipp to average between 40-50 IP with Veras and whoever else in the 30 range.
Qualls and Fields both missed time with injury, Sipp joined the team in May or so and still had 50 IP. Veras joined the team in July or so and pitched 32.
I'm not sure why I care enough to go into this, but the innings you expect simply wouldn't work for a modern pitching staff. You've got 7 relief spots, and 5 starters. If Veras and the 7th guy each throw 30 innings, and Gregerson, Neshek, Qualls, Fields and Sipp average 40-50 (so let's say 45), that's only 285 innings total from the 7 bullpen spots. Obviously there will be more than 7 guys over the course of the year, due to injuries, demotions, etc., but I assume you're not counting injuries; you and HH are just talking about expected usage of each pitcher based on need/ability/durability, correct?
The Astros staff threw 1,438 innings this year - just under 9 per game. If the 7 reliever spots only have 285 combined IP, that means the 5 rotation spots need to average 230 innings each, which is over 7 IP per start. That's simply not going to happen in this day and age (Keuchel, even with 5 CGs, averaged just under 7 per start, Feldman and McHugh, just under 6 and 1/3).
So the bullpen needs to pitch about 450-475 innings, even if the starters average 6 IP per start. That means the 7 relief spots average 66 IP each. You figure you might get a little more out of a long man, but in general, the better relievers on the team are going to have to pitch 60-70 IP each, barring injury.
Bottom line, there will be plenty of innings for Gregerson and Neshek if they're healthy. Nobody's expecting them to be Mike Marshall, but we should absolutely expect them to rack up 60-70 innings.