Vomitting multiple times a night for over a month

Thanks for any assistance in advance!

I have a 9 year old Persian who has been vomiting 3-4 times per night for around 6 weeks.  9/10 the vomiting occurs between 2am-7am and is usually more bile than it is containing food.  She typically will throw up once and then five minutes later throw up a smaller amount of "foamy" bile.  

Pumpkin is in good health according to the vet, she's still playful, has good energy and has normal bloodwork as of 3 weeks ago when I took her in.  The vet recommended trying grain free food, which I purchased, but it hasn't seemed to help.  She's still playful, has a very healthy appetite and keeps herself hydrated, but continues to throw up.

Some quick points:

- I did recently move, just before this activity started.  With everything being packed up and then upacked, it could be possible she swallowed something which she can't get rid of

- She typically throws up in the master bedroom, and there is a significant amount of "popping and dripping" type noises due to the new construction of the home, so I don't know if that's causing her stress

- Her stool has not consistently been solid during this time, it tends to be closer to a diarrhea and not the more typical well formed stool. 

Although she has done this at times in the past where she'll go a few days of throwing up and then I'll give her wet food (mixed with some laxatives) and she would typically relieve some of her constipation, but at this point it's gotten pretty severe.   I'd be happy to provide additional information, but would love any advice anyone might be able to provide.  Thank you!! 

Couple of questions...even though she seems to have diarrhea, how often is she going?  Could she still be constipated? I know that sounds crazy, but sometimes one can be constipated, and once it gets going, it's actually diarrhea, at least in humans.  Also, WHAT food did you switch to...brand, type, etc.  (please be very specific here)  And lastly (for this round), when you say "frothy bile", are you meaning it's a dark greenish brown, or almost clear?  When I think the frothy vomit, I think clear...when I think bile, I think dark greenish/brown .  The frothy clear is usually indicative of too much stomach acid.  My old girl gets that, and I keep some treats under my pillow and give her a few a couple times during the night to keep her from doing that early in the morning.  Pepcid A/C works for that too, IF you're good at pilling .

If you or your Vet suspected she might have swallowed something she can't get rid of, did you get an xray done?  Somehow I don't think she would keep eating if she had a blockage, and I really don't think she would be throwing up at the same time each day if she had a blockage, but I guess anything's possible.  You feed her more than once per day, though, don't you.  If not, then it would be more of a possibility, although I wouldn't think she'd be interested in eating much if she truly had a blockage. 

Have you notified your Vet that this is still happening since you took her in 3 weeks ago?