Well, the EU trade agreements are very influential on investment. Something like £450 billion of FDI is from EU firms. Secondly investment is already stalling as firms like Siemens wait to see what will happen.
Your points on productivity, I dealt with above. With falls in internal and foreign investment you will see initially less short run economic growth and in the long run the productive capacity of the economy will not increase. So will the SR effect productivity is likely to fall.
Firms don't increase productivity when the markets that they operate in are contracting, on top of this they don't invest much in human or physical capital, again reducing productivity.
On top of this increasing costs due to increasing inflation is likely to further damage the economy.
The UK will be able to strike trade agreements? How long do these take on average to organise? Why do you think that they will be on our terms?
If we go to the WTO standards we have to offer the same deal to all 160 countries in it unless we organise preferential deals outside of this, which again takes a long time. The US deal will be far more like the TTIP deal you want to avoid than the one the EU is negotiating due to a reduced negotiating position.