"Glamping" usually means higher prices. For economy lodging I recommend going to the website for the official concessioner, Xanterra, at www.yellowstonenationalparklodges.com
There are cabin accommodations with either Shared Baths or ensuite baths at Roosevelt, Mammoth, Old Faithful and Lake Lodge. There are en suite cabins at Lake Hotel. The cabins at Roosevelt tend to be smaller so you might need 2 cabins. Will people be OK sharing a bed? There is not enough room in these cabins usually, to lay out a bedroll.
Here's how I would lay it out:
July 8: Arrive Bozeman - What time?? That will dictate where you would spend this night. Overnight Roosevelt, Mammoth or in Gardiner MT (gateway town) if you get in early enough you can drive a couple hours before dark.
9: Overnight Roosevelt, Mammoth or in Gardiner MT (gateway town)
10. Overnight same
11. Overnight Grand Tetons - maybe Colter Bay might have something in your price range
12. Overnight same
13. Overnight Old Faithful Lodge (cabins and less expensive than the iconic OF INN).
14. Overnight depends on what time you leave tomorrow
15. Depart Bozeman
This is 7 nights. You said 7 days but people often mean 7 nights. IF you just have 6 nights, you can cut one of the nights on the Northern end of the park.
Be sure to book in park lodging ONLY at the above website. There are a number of 3rd party bookers who sound official and come up first on a google search. They charge a 10% booking fee.
Book what you can. IF your choices aren't perfect check daily until something pops open. I decided on a last minute trip for June last month. I got 1 room for 2 nights but needed 2. I booked what I could and then watched the website daily and within 3 weeks there was a vacancy that I needed but you need to jump on them right away.
Once you have your lodging booked I can help you with a daily itinerary. It's too hard to do an itinerary when I don't know where you are staying as there are so many variables. This spread of nights gets you thru the whole park.
And thank you Kate for the ping!