If I am confident of finding future mortgage payments (in 3-4 years’ time) from my monthly income/savings, should I do a full OA to SA transfer now and continuously empty my OA balance into SA?

But the bigger environment is out of our control.... that is a risk... do buffer some spare funds of 6 mths

OA to SA transfer is irreversible. A better option might be to utilize your CPF Funds for investment under the CPF Investment Scheme(CPFIS). This has a twofold advantage:

Firstly, you will be potentially able to earn a higher interest rate than that of CPF SA's 4%.
Secondly, you can only invest CPF OA monies beyond the first 20k of your OA funds. In this manner, you have a security net that touch wood, in case anything negatively impacts your income and subsequently affect your abilities to make mortgage payments, this 20k can tide you over easily. In the worst-case scenario, the 20k runs out and you can resort to liquidating said investments.