You can't install a 10-30R. That's off the table. The question is whether you can
- install a 6-30R with hot-hot-ground wires, or
- run hot-hot-neutral-ground wires and install a 14-30R.
You need to check this. But most likely these machines are 220V-only and have no need for neutral. If so, those machines should not have had the 10-30 plug on them in the first place, because 10-30 provides neutral but not ground. This is very common with hobbyists who simply want to 'get-r-dun' and don't want to care about safety or Code (which are close to the same thing IME).
Those machines probably want 6-30.
10-30 is bad news because it lacks ground. Neutral is not ground, and grounding things to neutral is unsafe.
Conduit is magic
Regardless, You have conduit, and I take that to mean the conduit is continuous from the service panel to the new receptacle location. Cable such as 10/2 cable, is definitely the wrong thing in the sense that trying to install it in conduit will be like wrestling alligators. It also destroys your ability to expand it.
The right thing to put in that conduit is
- Two black wires, type THWN-2, size #10, stranded. *
- One bare or green ground wire, #10, pref. stranded
Pull those through and you'll have everything you need to hook up a NEMA 6-30, which is I believe what your tools actually need. Now if I am wrong and a tool actually needs neutral and NEMA 14-30... or if later on, you want to hook up a new thing which needs neutral, or you just want to future-proof, nothing easier: Leave the wires in place and pull 1 additional wire:
- One white wire, THWN-2 #10, stranded
To pull it, you can try bundling the ends with tape and pushing it through, or use a shop-vac to pull through a napkin tied to a stout string. Anywhere you gave yourself a conduit body to pull through, open that up and guide the wires through, don't drag 'em around that corner. You can also use fishing tape.
You notice this leaves you lots of room. You can actually put as many as 4 circuits in that cable. The circuits could be larger - you could support three more 50A circuits (#6 wire) or even a mix of bigger or smaller. So in fact you don't even need to swap plugs, you can simply throw another hot-hot or hot-hot-neutral in that pipe, and power a separate plug, and you can run both at once. Real handy if you get a 240V dust collector. These multiple circuits can share the 1 ground wire.
It's not actually illegal to run cable in conduit, just a very miserable experience to pull it, and the cable chomps most of your pipe capacity (flat cable is counted as if it is round wire of the widest dimension, which means only 1 cable in a 1-1/4" conduit). And you wouldn't be able to do modular upgrades like this - if you had pulled 10/2 and wanted neutral, you'd need to yank out the 10/2 and pull 10/3, what a waste. The upshot is, whoever told you to use cable is a fool.
All this to say: grab the 10-30R and the cut cable and take it all back to Lowes, and at the customer service desk be angry.
You already did it!!??
Edit: Now you are telling me you already have a 6/2 cable and a 10/2 cable stuffed into this conduit.
OK let's do the math. Your 1-1/4" trade size conduit has 1.5625 square inches. Oval cables count the same as a round wire of their wide dimension, 6/2 is 0.68" across so 0.4624 square inches. 10/2 is 0.49" across so 0.2401 square inches. Both cables (so far) count as 0.7025 square inches. That means your conduit is already 45% full. Two "wires" in a raceway are only permitted 31%, so that's already illegal overstuffing.
3 or more wires can fill to 40%, but the two Romex already put you over 45% so that's no go. There is no way to do this. If you want to add a third circuit you must yank out all the Romex and substitute THWN, which will be insanely easier to pull, by the way, especially if it's stranded.
Once again: You see it at Lowes/whatever where they often have pre-cut lengths of cable at a discount, even though Lowes supposedly has a no-cut-cable-return policy. This is where those come from. Tear out all that cable, take it and everything else on the receipt back to Lowes, slam it down on the table and let the Hulk rage: "You knew this stuff was illegal when you sold it to me!" Leave em all the stuff, tell them you are going to chargeback your credit card for the full charge, and then do it. Doing a chargeback costs them about $20 and they lose the money too.
If you have things on the receipt you want to keep, just buy clones on another receipt, and return them on this receipt, so you're returning every single thing on the receipt. I do it all the time because I get reimbursed, and accounting dosn't like to see two complicated receipts showing buying A B C D E and returning -A -B -C.
And when you buy replacement cable, I'd go to an electrical supply and tell them you're not impressed with the prices or service at big-box (say that so they know you are price-motivated and will give you a contractor price). The electrical supply will have more variety of colors for your circuit-distinguishing pleasure.
*Why the same color? It's not really necessary to distinguish the two hot wires from each other - seriously, you're not going to do anything with that knowledge! Also, feel free to use other hot-legal colors (NOT green gray white) especially if you are mixing several circuits in this pipe.
So if you heavily populate this with four 30A circuits, use black-black, red-red, blue-blue, and orange-orange (or whatever your electrical supply stocks).
I had one genius put four #10 circuits (and some #12 circuits) in two parallel conduits. (4 circuits per conduit max). He put all the #10s in one conduit, circuit 1 was black-red and so were the other 3. His markings fell off, and you couldn't tell 'em apart. So I "rearranged" - 2 blacks and 2 reds in each conduit. And made the circuits black-black and red-red. Now it's easy!