So, after some discussion it seems we've more or less settled on three immediate objectives:
1.) Take Logan's Run.
2.) Deal with Lolly Cholly.
3.) Grind Random Encounters.
I propose we start planning for these now, to speed things along a bit.
For Logan's Run, I think we should go for the throat with a decisive, stunning victory with an invisible insertion of crack troops inside the garrison.
Even if we don't immediately take it, making all the troops on the walls our prisoners, (Marbit, is this even a possibility?)
the disarray this would leave the enemy troops in should still carry the day for us. The enemy won't be expecting this tactic, (Nemo should have agents watching the Archons by then, so not even Charlie will see it coming) and if it's ever going to work it'll work on a level 1 city.
More detailed/specific plan
Most of our force here will be just one big distraction. We would bring overwhelming force in against one side of the walls, drawing the enemy out of the garrison. Uncroaked infantry would go in first to soak up hits, immediately followed by archers to supply counter-fire. Then we'd send in the rest of the infantry and the sappers.
Meanwhile, an elite force would sneak around from the rear. One stack mounted on Balrugs (we'll need to pop a second one) accompanied by all of our fliers save the brickbats, all made invisible by Nemo. They'll enter the hex from the west or southwest, where they won't be expected. (In fact, they won't even move with the main column, so the enemy will think they know where our entire army is.)
They'll fly over the walls, taking the enemy garrison by surprise. At best, they've made all enemy units into our prisoners, at worst they can open a gate for our army to sneak in through.
We'll still need some concrete intel on Logan's Run before we can move, though. Specifically, a map of the city and the area defined as "the garrison" is something we must acquire.
As for Lolly Cholly, just having a plan to take him out would give Yuri something concrete to work on for negotiations... (And no discredit to Yuri, but that's really a long shot.)
Here, I think that brute force would be most successful. T. Coil would go with this group, and be their "better battering ram". Since it's a fair distance away, and the tunnels restrict archery (assuming we're using the revised LOS rules), we'd probably send only units mounted on Naughty Kitties and Heck Pups this direction. Unless we got the Balrugs to ferry additional units over before the battle of Logan's Run, although these units would be unable to retreat as far as the rest if Lolly turns out to be a much bigger threat than expected.
Whoever isn't part of one of these two taskforces will be stationed at Dis City, in case of a second siege there. In the meantime, they can go on hunting trips and grind for XP. They could even camp outside the city if they wish, as long as they can get back in 1 Turn.