I'd scrap this whole plan and start over (save for the existing buried conduit)
You started off on the right foot by burying a conduit from the house to the shed, and you are also correct that NM is nogoodnik in a wet environment, so we'll be replacing that as you indicate. However, you were only familiar with the cables (NM and UF) used for building wiring, so you figured that was what was used inside conduits as well, and then discovered to your dismay why that isn't so: they are stiff, chunky, and generally utterly miserable to pull down conduit.
As it turns out, what you need to be pulling down these conduits are individual THHN/THWN wires, not the cables you're used to. These take up far less fill than a fat, stiff, miserable cable, and are also far easier to pull down conduit, with their slick nylon outer coating and stranded cores giving them superior flexibility and slipperiness.
Going cable-free across your attic
One other faulty assumption you made was that you must transition from conduit to cables when you head inside. In fact, that's not the case; there's even a handy form of conduit that is basically purpose-made for light-duty indoor work. The Code calls it Electrical Nonmetallic Tubing, or ENT for short; however, it's much more commonly known as "smurf tube" for its bright blue color. It is made from thin PVC plastic, corrugated for strength and flexibility, and is legal for mains wiring within houses, although it's most commonly used for communications/low-voltage work.
With this, we can make the run (save for the dryer) entirely in conduit, allowing us to take a junction box entirely out of the picture, and giving us much more flexibility in locating the remaining box for where the dryer circuit exits the conduit.
As far what goes inside said conduit...
Your other issue with your plan for powering up the shed is the idea of running two separate branch circuits there, instead of simply fitting a subpanel at the shed and running a feeder to it. Given that your 1.25" Schedule 40 PVC can handle 374mm2 of wire fill, we can fit 3 1/0 Al XHHW-2 or THHN/THWN wires alongside an 8AWG bare copper ground down it with room to spare for 3 10AWG THHNs and a 10AWG bare copper ground for the dryer. However, that's overkill for the initial portion of the homerun, and 1.25" ENT is rather scarce on the ground for that matter.
This means we're better off running 3 2AWG Al XHHW-2 wires alongside that bare 8 AWG copper ground, giving us the ability to provide 90A (or 100A with some pigtailing trickery at each end) to the shed, while still being able to use 1" ENT for the run across the attic. The 4 10AWG THHNs for the dryer run out from the panel wil easily fit into the 1.25" PVC alongside the proposed feeder, and you can simply use a T-body, a reducer, and some 1/2" ENT for the rest of the dryer run. (If you wish to transition the dryer circuit to NM at a box in-line with the 1" ENT run, you could do that as well; I simply suggested using the ENT for the dryer run because it means you don't have splices or boxes to worry about.)
Once you get to the shed...
Once our wire run reaches the shed, we then land it on the line lugs of a 100A, 24-space, main breaker subpanel. This provides us with a convenient main disconnect for the shed, and also plenty of space for future expansion. In the subpanel, then, we can fit the breakers for the sauna heater and lights/outlets there as well. Note that you'll have to pull the bonding screw/strap (or make sure it's not fitted) and fit separate ground bars if the panel does not come with ground bars factory fitted. You'll also need to torque all the breaker and panel lugs/screws to spec using an inch-pound torque screwdriver or torque wrench, by the way; this is the new 110.14(D) requirement in the 2017 NEC, and is also a good idea anyway, lest your panel get a case of the loose lugnuts.
As to replacing that NM...
What I would do to replace the NM is fit a junction box at where the conduit terminates, then run individual 14AWG THHN hots and neutrals + a 14AWG bare ground down the existing conduit, and then continue the runs from the inside junction box with NM. Note that you may have to replace some of the NM inside due to water wicking up the paper separator in the cable.