Feeling the heat
While your conduit can physically fit all those wires, sure, there is a problem with your plan still, and that's the amount of heat stuffing 16 current-carrying conductors into a conduit throws off. In fact, due to the inability of the conduit to dissipate that much heat, the NEC limits your 10 12AWG wires to carrying a mere 15A per wire and your 6 14AWG wires to a puny 12.5A each, based on the derating factors from NEC 310.15(B)(3)(a) and its associated table.
One solution would be to upsize the wires to 10AWG for the 20A circuits and 12AWG for the 15A circuits. However, that would limit you to 7 10AWG (the existing 20A circuit, the existing spare circuit, and a single 20A MWBC) wires and 4 12AWG wires for the two existing 15A circuits, as well as a 10AWG bare ground wire (which must be bare, or else you'll overflow fill).
Consolidation is a better plan, here
However, this sort of situation (a shared homerun conduit) is where Multi-Wire Branch Circuits shine, as we can split each MWBC into two independent circuits before we reach the kitchen GFCIs, yet run 2 circuits' worth of power over 3 wires, of which only 2 count as current-carrying for derating purposes, as the neutral in a MWBC only carries the difference in current flow between the two (opposite leg) hot wires.
With this, we can get 6 20A branch circuits run using just 9 wires (vs 5 branch circuits run using 10 wires) and still have room for the 2 15A branch circuits (using 3 wires instead of 4). However, it requires the use of two-pole breakers in your panel (or handle ties if you don't have GFCI at the panel, but two-pole breakers tend to be easier to find), in order to provide a common maintenance shutoff for the MWBCs. You'll also have to pigtail neutral at any receptacles that are on the MWBC portion of the circuit, but that does not appear to be a concern here, and you'll need to distinguish the various neutrals as well.
Fortunately, since you're working in conduit, striped THHN is a readily available solution to this issue. I'd have the plain white neutral be the 14AWG wire, and then use yellow, red, and blue striped wires for each of the 12AWG neutrals, with black hots for the 15A MWBC and matching colored hots for each of the 20A MWBCs.
One other thing you will have to deal with is the box fill at each end. The existing junction boxes that terminate this conduit run are 4 11/16" by 2 1/8" square boxes, with 42 in3 of fill. While more than adequate for your existing run, which only takes up 36.25 in3 of fill at each end (8 12AWGs, 8 14AWGs, and a 12AWG grounding allowance), this isn't enough space for any of the proposals you are floating, never mind filling your conduit to the brim with MWBCs.
The simplest option for fixing this would be to add an extension ring to both boxes -- a 4 11/16" square by 2 1/8" deep ring adds another 42 in3 of fill to the picture, giving you ample space for even the most extreme conduit cram job possible here. If replacing the boxes outright is an option, I would go to a large/deep metal two-gang or three-gang box as it provides better access to the wiring space than using an extension ring would.
Furthermore, keeping all the splicing straight will likely require doing it in an organized fashion instead of simply wirenutting seemingly-matching wires together and hoping for the best. Fortunately, Wago offers DIN rail carriers for their 221 series lever-type splicing connectors -- look for Wago 221-500s, although you may need to order them online as they are not commonly stocked here in the US. This, along with some Wago 221 lever-nuts and a few inches of DIN rail screwed into the back of the box, lets you do all the wire splicing in a neatly organized manner, much akin to having a set of terminal blocks you can use.