Getting better
If the mobile mechanic is 100% certain the timing is absolutely spot-on then you need to delve a little deeper..
Did the mechanic reset the timing with the crank , cam and pump properly pinned? I ask as it's critical the crank is properly pinned even though the index hole in the flywheel is hard to reach. If you don't it's still possible to be a half or even one tooth out and that can make all the difference. "Eyeing" the crank keyway to set the timing is not accurate enough, especially when you know it was out to start with..
If you and he are certain the timing is right, the next thing is to carefully check valve clearances. White smoke means that unburned fuel is present in the exhaust and the usual culprit is low compression on one or more cylinders. This would also account for lumpy running. A check of valve clearances should show if any of the valves are unhappy. Any that are way off the normal range may be indicative of being bent.
Valve clearances are 0.15mm - 0.25mm Inlet and 0.35mm - 0.45mm exhaust when cold. They are adjusted by shims.
If all valve clearances are about right then consider having a leakdown test performed to check the compressions are good.
Take it for a run by all means as a bit of white smoke when the engine is cold can be nothing to worry about but there should be none at all when the engine is hot and under way. A run just might settle in a valve or two if they are not currently sealing quite 100%.
Sadly, I suspect you may have slightly bent valves or a damaged valve heads/seats as a result of the timing being off.
I hope I'm wrong in my diagnosis.....