TD use Equifax for credit checks, AMEX use Transunion and Chase mainly use Equifax but sometimes transunion. The inquiries on one bureau won't appear on the other (Except for Cap 1). Personally if I were applying for these 3 cards, I would do TD and Marriott at the same time on different browsers and Amex after or before. From my experience, I have done up to 4 Amex applications in 1 day and received only 1 hit on my transunion file. All approved. Some websites suggest Amex only does a soft inquiry if you are not approved.
If your score is 700 + more than likely you will be approved. Amex is a bit stricter with their credit cards than charge cards.
I don't think applying through GCR or RFD would matter when it comes to the approval rate. Your credit worthiness (score, debt ratio, number of inquiries etc.)would matter most.