Hi A.D.
I think a mortgage professional (mortgage broker) would answer these questions much better than we can so it would be worth contacting one at some point.
The larger your deposit, and the smaller the loan-to-value of the mortgage you want, the less risk there is to the lender. A 50% deposit should therefore much improve your chances.
There's no general rule that you have to wait three years after a trust deed to get a mortgage, it just so happens that's when (for many people) it will no longer appear on their credit report. A lender that's especially interested in whether a borrower was ever in a trust deed can still require disclosure on an application form once it no longer appears on your credit file. Other lenders seem to care less, we've had several posters report that they've been able to get mortgages within less than three years after their discharge. It's all down to the lender.
Different lenders will also require that the mortgage is fully repaid by different ages. If you want a mortgage that runs beyond the usual retirement age you'll need to find (maybe with the help of a broker) one that is amenable to this. Be ready to demonstrate how you'll be able to fund the repayments if you'll no longer be working.