I would buy a kettlebell that is heavy for you and do the following complexes with it (in different workouts)
Complex 1 -
One handed snatch
Drop into a swing
toss to other hand at head height in the swing
Repeat other side
Complex 2 -
one handed clean
2 push presses
drop from the top position of the second press into a swing
toss to the other hand at head height
repeat with opposite side.
Do these on non-consecutive days
Day 1: complex 1
Day 2: complex 2
Day 3: rest
Do them for density training. First workouts do them in increasing sets with 1 minute rests. So a set of one (per side), rest one minute, a set of two (eg. Left hand snatch swing/toss, right hand snatch swing/toss, Left hand snatch swing/toss, right hand snatch swing/toss, rest), then rest for 1 minute and go up and up and up until you find your max. Lets assume your max was 10, density training says take your max and do 4 times the volume total, so 40 reps total. So your second workout do 8 sets of 5 with 1 minute rests, when you can do that do 7 sets of 6, 6 sets of 7, 5x8, 4x10, 3 x 15, then go for a new rep max the following workout and repeat.
When you can do 50 reps with both complexes, sell your kettlebell and get a 10lb heavier one. or throw it away and get a heavier one, you'll still be spending less than a thousand bucks.
By calisthenics I mean pullups. Do pullups. Get good at pullups. Do tons of them. If you cant do 50 work on that first. If you stall, switch to doing weighted pullups for a sets of 5 reps (avoid 1 rep maxes for pullups, I think there's a lot of cheating in doing them). Your goal is a double bodyweight pullup, and 50 unweighted pullups. Then you can start working towards 1 handed pullups.
Lunges are good too, you can do them holding your kettlebell for reps.
A sample routine might look like
Monday - Complex 2, Pullups, Turkish Getups
Tuesday - Complex 1, lunges, planks
wed - rest
Thursday - Complex 2, pullups, Turkish getups
Friday - Complex 1, lunges, Turkish getups
Sat & sun - Rest.
And the best part is, a 56lb kettlebell will cost you like 100 bucks, take up less space than your dumbells, and can be sold, traded in, or thrown away much more easily... and that's all you'll need.
WHEN YOU HAVE GONE AS HEAVY AS YOU CAN BUY WITH KETTLEBELLS, and you have a 120lb KB and you're doing 50 reps with my complexes above, you can always do something like 2 snatches, then swing/toss to the opposite hand, or clean, press, press, clean, press, press, swing/toss to theother hand.
But that's so far off you really don't have to worry about it.
I promise greater strength gains from following that program than using your heavy dumbells in lieu of barbell training at a gym. on the surface it looks like a kettlebell conditioning routine, but strength and conditioning are not always either/or. you can develop a level of the former through loading the latter.