Totally agree with pp, definitely a good idea to get a hold of the books.
At 7 months, most babies are having 2 x long naps. A long nap is really preferable, because it is more restorative. 45 mins naps are a pretty good sign of undertiredness, and 1.75hrs awake time is very, very low for his age so I would start trying to push his awake times just 10 mins at a time until you can get some longer naps. Most at 7 months can manage 2.75-3hrs awake between naps.
As a guide, an ideal routine for 7 months old would be something like:
7am A/E
9.30am S
11am A/E
2pm S
4pm A/E
7pm S
As for breaking the prop of sleeping on you, I would try PUPD. Some overtiredness is pretty much inevitable when you are weaning props, but once he can sleep independently he will catch up.