OK since I brought it up, I guess it rightly rests with me on how to do it, right?
What do you have for equipment out behind the shed? What size boxes. You can do over/under with QE between them. Or go side by side in a divided box with a shared shallow box above a QE above them.
( QE = queen excluder )
Think over what you have for equipment and what your preferences are. Select the path that you are most comfortable with. (Slow growing package/nucs or DQ booster rockets)
As for tips tricks steps, I hope the below is understandable and makes sense;
You can combine the established queens. It is the basic colony combine with newspaper and a QE between them. The extra step I do is spray the paper with sugar water that has a fairly strong dose of honeyBhealthy in it. The paper goes on top of the bottom colony, spray it. Fold over two opposing corners of the paper, but about 1/2". Just enough for air circulation and a few bees able to pass through. Put QE on top of paper, spray it. Put second colony on top. Put the lid on. No upper entrance. Leave them completely alone for 10 days.
The new caged queens do not DQ right away, she will need her own box for a brief time to get her started first. A candied release up above might work but I would not try it.
I see above you have 10 packages installed about 3 weeks ago. So will assume 10 singles. The details of the way I would do it in your yard is:
Combine 8 of the established package hives into DQ over/under. Note no upper entrances, all traffic goes through the bottom. While combining I would be stripping away half the bees and 1 brood frame from each of those and putting into 4 separate boxes which become fairly decent queenless splits/nucs. The bees for each of the splits will be coming from two hives so spray them down with that hBh laced sugar water to stem fighting and just shake hem in. You will end up with 4 DQ hives, 2 regular hives untouched, and 4
new queenless boxes. Then, as normal, cage introduce the 4 new queen arrivals each into her own queenless box. A week to 10 days later once the new queens are accepted, released, and laying a bit you can leave them as is or then combine those as well into over/under DQ to further boost bee production.
Tips/notes: Place the 4 new queen boxes in the set location that one of their parent package colony bees came from. Because there will be some bee drift from the DQ hive back to that spot and vise-versa.
Beeyard before the work.
S S S S S S S S S S
(( S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 ))
Beeyard after the work
S S D N D N D N D N
(( S1 S2 D34 N34 D56 N56 D78 N78 D910 N910 ))
(S=single, D=double, N=newqueensplitbox, numbers in (()) are shown with colony numbers to illustrate who goes where)
Thus the stage would be set. Then just wait and watch the show. The boxes will fill with bees quickly. Stay on top of weekly inspections of both upper and lower nests to keep them inline and progressing. Treat each nest as you would any other single hive when you are inspecting it, except do not move any brood frames around between them, so you can actually see what each queen is doing and able to assess them. If you move brood around you will loose track of whose patch is whose and have no basis for your queen performance evaluations. Separate the DQ into individual hives sometime later, before they get too big to manage.
The queens just lay the eggs. The bees make the bees. More bees make more bees which make mores bees which make more bees .... Whenever we are flush with queens but short on bees the obvious solution (to me) is to DQ to get each queen enough support staff to show her excellence or mediocrity.
Do what you will with your bees. You are responsible for them. I have merely laid out what I would do for your considerations.
Hope that helps!