When derating for wires in conduit, do you round up or down

You're barking up the wrong tree. 310.15(b)(2)(a) isn't the issue, you are a ways from hitting that. The issue is the other kind of conduit fill.

With conduit fill, you are limited to 40% of the conduit cross-section with 3 or more wires.

The company gave you a 1" knockout and they are correct. You need to bring in six #6 wires and 1 bare ground wire up to #6. That will only give you about 33% conduit fill on a 1" conduit with THHN wires.

There is an additional rule that oval cross-section cables are treated same as a round wire of the maximum dimension. #6 Romex is .68" in the long dimension so it is a wire of .68" diameter. That is 0.363 sq.in. in surface area, triple that is 1.09 si. Divide by 40% you need a pipe with 2.7 si. A 1.5" pipe isn't close, so you need a 2" pipe.

Needless to say, trying to stick three cables in a 1" knockout is a lost cause. It will never be legal. It will never be anywhere near legal. It will always get redflagged by the inspector. That is what he is trying to tell you, and you are misconstruing this to be a 310.15(b)(2)(a) issue. It's not.

Again, this is easily done with conduit. I happen to like EMT conduit because it's a good balance of "easy to work with" and "allows the conduit to be the ground, so no ground wires needed".

How to solve it

Given that running conduit back to the panel is not a possibility, what remains is to run 1" conduit to an intermediate point or point(s), and splice from your cable to THHN wires at that location. Each cable will require 20 cubic inches of splice space. In addition each box will require 7.5 cubic inches to allow for cable clamps and grounds. So if you can get one big box with 67.5 cubic inches, that will do. Or one with 27.5 ci and another with 47.5 ci.

One 6x6x2" box should suffice, or a 4-11/16" square box that is either deep with a domed cover, or has a box extension.

Ironically, you are at a disadvantage getting a big box at a big-box store - a proper electrical supply house will have better selection and be cheaper.

And here's a relief: you don't need to buy 2 colors of THHN wire. You are not paralleling, so you do not need to distinguish red from black - black and black are perfectly appropriate colors for a 240V circuit. In fact, when dealing with multiple circuits, it is far more important to distinguish circuits from each other.* So grab a 5-pack of colored electrical tape and call it golden. The 3 circuits can be black-black (unmarked), blue-blue and yellow-yellow.

Seriously, you don't want to accidentally attach one of the 3 heating coils to Black1 and Red2. It will seem to work, but will cause weird problems and would trip a GFCI if the supply breaker was GFCI.

Stuff that doesn't matter

As far as 310.15(b)(2)(a) first that's a non-issue in conduits shorter than 24", but even so, every circuit fed from a split-phase panel counts as 2 conductors. Because it is concerned with heat, and grounds don't matter, and neutrals between 2 hots do a magic thing that cancels out. So you have 3 circuits, therefore 6 conductors. 6 conductors gets an 80% derate off the highest temp rating allowed for that wire, and NM gets an exception allowing it to pull from the 90C column even though it's 60C wire. So at #6 you are reading 310.15(b)(16) and getting 75A, derating x 80% = 60A. Which is a big nothingburger, because #6 wire is already limited to a 60A breaker (actually 55A but that size isn't made, so you get to round up.) Now if you had 8 conductors, that's a 70% derate and #6 gets knocked down to 52.5 amps.)

Also in the "doesn't matter" category, their three 40A breakers actually call for #8 wire, but this changes nothing. Three #8 cables still can't fit in a 1" knockout/conduit, and three #8 wires fit with ease. So using #6 wire has no impact.

* I have one installation where the guy ran 2 1" conduits from a panel to a machine room. In one of the conduits he put four 120V circuits. The other got four #10 wires for 4 circuits - red-black, red-black, red-black and red-black. And you can't tell them apart because his cheap labels fell off. Ugh. I plan to rearrange it to black-black and red-red in conduit 1, ditto in conduit 2.

Don't replace metal pipe with PVC "just because it's what everyone uses today". Metal pipe is superior in every way. And may also provide a valid earthing path.

You should not use cable in conduit. You should use individual wires which are rated for pulling through conduit. For instance, North America uses THHN, which has a nylon outer coating to make it slick for pulling. Surely any wires sold as individual wires will be made for this, because it will obviously be used in conduit!

All curves in your conduit should be broad turns. If you have sharp corners, there will be a removable cover to access the wires. You do not drag wires around corners - you remove the cover, pull to there, then pull the next segment.