I think $2 billion would be enough for a major expansion. I can see 2 relatively easy options for extending the Epcot line.
Choice 1 (the cheap choice) would be to extend the Epcot line to include a BC/YC stop, a Swan/Dolphin stop, a HS stop, a Blizzard Beach stop, a Kidani/AK Lodge stop, and an AK stop before reconnecting to the existing Epcot line. They could even include a Cor Springs stop if they wanted at the convention center. This would just be a continuation of the one way single beam.
The problem is with all those stops it would take forever to get anywhere, buses would be faster. For example, getting on the monorail at GF to go to AK would require a stop at Poly, TTC to transfer, Ep, BC, Swan, HS, BB, AK lodge, and finally AK. Even if each stop only took a couple minutes you'd probably spend more than 30 minutes sitting at stations on top of the travel time.
The better option (but much more expensive) would be to put another transfer center at Epcot and make the 2nd line a circle with 2 beams, this would help because you could go in either direction and skip most of the stops but in the example it would still mean getting on at GF, stopping at TTC and transferring, stopping at Epcot and transferring, and then AK. Much better but I still think a bus sounds more convenient.
Using the distance feature on Google earth shows this would be about a 10 mile loop. The current Seven Seas Lagoon loop looks to be about 3 miles and the TTC Epcot loop looks about 8 miles.
Here's a crude drawing of the circle line.
