The only difference is that with an inground pool, the pump uses effort (suction) to pull water from the pool, underground, then "up" to the equipment pad. So water flow isn't as effortless as with an AGP where gravity does the work. In your case, this means the two suction lines you have must be full of water to the pump to create a good suction (air-tight) so that water can flow constantly from pool to pump. Sometimes there is a blockage, but you seem to have ruled that out because you physically pulled (vacuumed) water from the pump side of that 3-way valve with your shopvac. So if we rule-out anytiing from the pool suction ports (skimmers) all the way to that 3-way valve, that leaves the pump and filter. The pump seems to be moving water, at least half a basket's worth, then goes dry. SO either it needs more time to pull water from your two suction lines, or there is an air leak somewhere around the pump. But you said all drain plugs have been installed on teh pump. I'm assuming the clear basket O-ring is installed too right? All lubbed well too for good seal? Is there any chance the MVP didn't get seated correctly on teh center pipe when you reinstalled it?
If none of this seems odd, the only other tihng I haven't asked .... when you fill the pump basket wiht water and turn it on, how long are you letting the pump run before shutting it off? For some pools, it can take a good 30 seconds to a minute to prime those two suction lines. You might even half to pull the water out of the basket, and refill it a couple times quickly to help prime the lines.