Ok, the current posts are posts are picking up 7' feet of beam load, x 550psf = 3850#, divided by 1500psf soil bearing, you've probably got 1'8x1'8 footings under your slab at those 2 posts. If you take out one post, the remaining post has a 1/2 span of 7 feet on one side, and 3.5 feet on the other, so the post is picking up 10.5' x 550# =5775#, which puts you back to a little under a 2'x2' footing. If you have your original house plans, and they show a 2'x2' footing under this post (not unusual, if you've got a builder that realizes concrete's cheap insurance), you're good to go. If it's only big enough to pick up the original load, you'd still have to saw up the slab and put in a 2'x2' footing. You'd probably have to beef up your original beam for doubling the span, but not as much as pulling both posts.
Pulling both posts may still be an option, do the garage walls sit on the slab, or on a concrete stemwall? If you're on a stem wall, and the beam ends land on a wall section at least 2 feet long, perpendicular to beam direction, you could still get rid of all the posts, or if you're at least 2 feet from the top to bottom of your foundation. If the garage walls sit on the slab, I'd dig down outside the building, and see how deep it is to the bottom of the footing. I'm used to seeing 1' below grade here, because that's the minimum here to prevent frost heave. As far north as you are, your frost depth is probably greater, which is a good thing for what you're wanting to do. Point loads on concrete spread at 45 degrees outward as they go down, so for every foot of concrete height, it spreads over two feet of footprint. If your concrete is deep enough to pick up all the loads at each end, a full length span would not involve any concrete work at all. If your footing is wider than 1 foot, you wouldn't have to be as high, since you'd spread more load front to back than a narrower footing. If you don't have your house plans, I'd do some investigating to see whats under there. It doesn't cost anything to do a little shovel work.
As for buying a permit, you're not in my jurisdiction, so I don't care. Your insurance company might though, and if you get caught, they usually double the fee of the permit for starting work without it. I don't know what the politics are like with the building dept. in your area, so I don't know how much of a pain in the ass it would be to deal with them. I know this can really vary over different places, but we help people with stuff like this all the time where I work. If you didn't pull a permit on the shop, and it's req'd in your area, you may be opening a real can of worms to get building codes involved now. They'd definately make you get that on a permit. Your contractor should've taken care of that, but as the land owner, you're ultimately responsible, so if he didn't, you'd be holding the bag. Some parts of the country consider outbuildings exempt, but they aren't where I live, unless it's an agricutural building. You can probably get away with it, but still use good building practice, it's your family's home.
