I thought that I would add a quick comment here as I think I have experienced the problems you are facing more recently than the more hardened pros above. I started windsurfing in 2006 and bought a Carve 145 with a new 6.5m Gaastra Pilot rig to which I quickly added an older second-hand Tushingham 5.7m sail realising that the 6.5 was too big for the conditions I was sailing in. I sail off the South coast of England near Eastbourne so it is often choppy with large shore break. Not the easiest place to learn I have to say.
I began to go out in windier conditions towards the end of 2007. The biggest tip I received was to do everything a little more quickly and a little more extreme than I had been used to in lighter winds. You have more time to adjust and greater margins of error when it is not blowing a hooley. When the wind picks up a bit I found that before I could react I was back in the drink.
The answer for me was to try to uphaul and get my feet in the right place quickly BEFORE sheeting in with the back hand a LITTLE bit to get the power on. This is what Roger told me and is now saying to you. This is all well and good if you are not rounding up into the wind which is exactly what was happening to me. Everything stalls, you go nowhere and eventually get dumped after fighting with the rig for a bit. So, ensure that the mast is across your body into wind and slightly forward in order that you bear away. The nose of the board turns off the wind and when you sheet in it begins to power up slowly. Once underway you can increase the power in the rig by sheeting gradually.
My problems did not end here I have to say. Once you start to power up the standard "7" stance no longer works, being too upright. You need to oppose the rig's power with your body not just your arms and this takes some adjustment. Leaning out over the windward rail, eventually in the harness, keeps the board flat, energy driving through he board and you dry, at least for a little while! I thought that I was doing this but my instructor kept on at me to make more exaggerated movements and eventually I got it. You may find that you over compensate and over adjust from time to time. It is a balancing act and you develop a "feel" for it.
Sounds like you are not far off and that a gradual upgrading of kit as you improve should help. The nirvana of planing and blasting is just over the horizon and I bet your face will hurt you will be smiling so much. Good luck.