Sibble,
I let my feeddogs up but have lessened the pressure on my presser foot. One of my machines has three settings, another has a "bolt-like" post that can be turned to tighten or lessen the pressure.
You can test the pressure by putting your presser foot down and then attempt to lift it by hand from the back of the foot. Obviously, if it is difficult to lift, you will need to loosen same. Because you have three layers going under the needle the machine will require a bit more space, thus lessened pressure in order for your project sandwich to flow.
To cover your feeddogs, I would hesitate to use any kind of tape over them owing to the possibility of the tape residue getting into my machine guts and gumming it up. I have heard of taping a credit-card like card over the feeddogs.
Ask me to clarify if this is not clear and helpful. Blessings, Suz