Start from the basics. If you've had someone look at it, and cleaned the carburetor out, that's a start. However, before they did this, they should have done the following, in order.
1) Drain the fuel tank/s completely and make certain there is no water at all present. If there is, get as much out as you can, then pour in a litre of metho into your first fill. (Metho mixes with water and petrol)
2) Check the oil, if it is in any way dis-coloured, ie: Milky grey and not black/brown and clean they you have a water leak into the combustion chamber and that may cause a miss. This will require a mechanic to diagnose and repair.
3) Next, I'd change over the fuel line. If it's been sitting for a bit, or the line itself is old, the bulb may be deformed on the inside, causing a vacuum in the fuel line and a stutter or stall when you try to rev it. Also check the bayonet fitting and that it's not blocked.
4) I would then check the fuel cap, and that it's breathing correctly. (You did open the breather valve right?)

If it isn't breathing correctly, it will cause a similar situation to a bad hose/bulb.
5) Check the spark plug/s, if they're very black it's not running correctly. Change them anyway. They should be a mid brown colour on the electrode, possibly a bit black around the top of the thread. If they're very white, it's running lean and will require a proper mixture reset. Same as if they're really black and gunky.
6) Check the spark plug lead/s and connectors. If the lead does come off the coil, clean and spray inside the connections with WD40 or a silicone water repellent.
7) You could also check the ignition/cut out switch to make sure it's got good contact. Hard to do without taking it all apart, but these can be known to break down on higher revs through vibrations.
Non of this is rocket science, and usually a simple fix. I find it difficult to believe a professional outboard mechanic wouldn't follow these basics to diagnose the issue from the start?
PM me if you still have issues and I may be able to help. NOTE: I'm not a qualified mechanic, but have lots of experience with my own Tohatsu 4stroke and motorcycles, where there's not a lot of difference. Also, I'm not on all that often, but do look in once or twice a week.