In the first video it appears the door is closing too far and reversing. If the door runs fine manually, balances when half way open, and doesn't drift down once fully open; I'd lube the door and reset the open / close limits.
I work for a company that installs thousands of residential doors every year. It's very rare to have a two-man crew for residential installs unless it's for custom wood doors, full vision doors, doors over 8' tall, or unusually wide doors. Premium 16'x21/24x2 insulated sections aren't that heavy.
That LiftMaster unit is okay but I wouldn't buy it unless I already had compatible remotes. Linear / Multi-Code is probably the best and cheapest path for adding remotes to a mechanical opener.
The newer stuff has radio learn buttons and the older stuff requires an external receiver which probably has dip switches. With LiftMaster an easy way to identify what type of opener you have is by the color and shape. If the opener is red, silver, or rectangle shaped, it's a logic opener and...
The 380UT remote shown above will accomplish what you want to do. Program one button for the 8500 and program the other button for the gate using dip switches. The instructions show how to program the remote buttons, it's very simple.
That remote requires programming before you attempt to pair it to the opener. Just a couple steps, the remote manual will show how to do it. Once it's programmed for the green button it will pair as expected.
You need to use very dense rubber or horse stall mat to isolate the opener from the punched angle. We do something similar on apartment buildings with underground parking to keep tenants right above the door happy. The same can be done on the horizontal track back hangs. Make sure your door has...
What remote are you trying to program? If you have a newer remote for Security+ 2.0 / Yellow button machines, it's not gonna work. You'll need a remote that allows you to program the remote itself for 890MHz / Green button machines. Something like a LiftMaster 893max or 380UT. If you have a...