As far as the access hole, there is no rubber plug. There's just an indentation in the backing plate where you can punch it out (in) and then install a rubber plug.
The "Knock-Out" is stamped into the backing plate and is designed to be removed, then yes, a rubber plug installed. The knock out is Hinged in the middle, both top and bottom, so go for the far ends with a nice large punch. No need for a cold chisel. Just position the punch on the tab at the end, then hit it. I have removed hundred of these doing brake jobs from the mid 60's going forward. Once they break loose on one end, grab it with side cutters and bend back & forth until it breaks off.
As other have said, make sure the "Star" wheel adjustor is free, perhaps some anti-sieze, but adjust and turn the drum until it becomes too tight for comfort, then back off. A small thin flat blade screwdriver is used to hold the advancing arm of, then turn the opposite way to back off a little. If your drums have NO outer groove, then they should still come off while rotating with your hands. On the back side of each shoe, there are 3 spots that the shoes backing plate (Under the friction) has a "V" shaped spot on both sides. The backing plate can wear in this area and create a groove so big, the shoes will catch on them. Replacement use to be normal, but a 4 1/2" angel grinder held just right can dress these 6 spots on the backing plate. The pads new have a cross-hatch pattern, but if ground of, still place a drop of high-temp brake lube on this area.
The park brake cable will stick inside the metal wrap housing before they stretch. Check this as well. Only one all-thread looking adjustor is provided while the passengers side, simply slide thru a semi-circle loop as to self adjust for both sides. Some axle grease will help this slider held to the frame by a simple wire hook.
As for a pedal that hits near the carpet, I would be check the front disc to make sure the calipers are rust free within the holding frame to be able to slide in and out. A wire wheel on both items with high-temp grease should always be applied here. If the stick bad, the inside pad wears first, while the out-board pad just sits there. Calipers can be repaired for $5 per side with a rebuilt kit. I you have compressed air, place a 1/2 - 3/4" piece of wood or metal plate on the out-board pads side, hit with air, piston comes out. We use that have races in the shop as ever caliper came apart. Once the piston is out, if chrome plated, inspect for loose plating or rust areas and replace if needed. The bottom of the caliper is the bottom of the bucket. This is where all of the junk collects, you will be shocked if these are original and wonder how they worked. Brake spray and green scotch-brite will clean the bore nicely.
The lathe-cut or flat seal goes in first, then using brake assembly grease, lube the seal, bore, then slide the piston inward. The outer seal has to be driven into place, just the outer edge. It really helps to have a seal driver. If rebuilt, or new re-mans, either way need the holding frame clean, greased and the caliper sliding with ease. The lathe-cut or flat seal will retract the piston a little as it twist when applied. It pulls the piston and releases the pads just enough to allow the rotors to move freely, but the pads are close by and do not require a long pedal travel to engage.
The brakes are a system and if one thing is wrong, it will effect the entire system feel and operation. This include the condition of rusty lines, hoses and especially any recent work.
I do not know Les Schwab, but techs who worked there do change. Some know more than others and maybe have not only more experience but ASE Certification / perhaps a Master Tech. I usually started my visual inspection of their work first to add in my ability to correctly diagnose the Root Cause and not just the symptom.
If you told them the (Customers Complaint) is the rear brakes did not work (Braking or park only or both) and they drove it with the pedal going near the floor, then charged you and they gave it back to you without a suggestion of proper repair, then I would not ever go back there again.
There is a residual line pressure device in the master cylinders rear brake port behind the metal insert to seat a double flare / inverted flare, that keeps about 10 PSI to keep the wheel cylinder cups inflated. The proportioning valve holds off rear brake pressure as to apply the fronts first, then rears second. It also moves an internal valve the effects you brake switch. It turns the light on with the park brake off. If pressure has changed so much, the light will come on, indicating a loss of pressure.
So if anything, due to my post, place understand there is a lot enfolded with brakes as a system and a lot for a Good Tech to know!
Please tell us and I will follow the "Thread". Best of luck!