You want to choose 36 games so you have 216 group slots to fill from 42 groups so your limitation of 'Every group has the same amount of games' makes your problem infeasible
because 216 is not divisible by 42.. In contrast many groupings/games seem to satisfy everything else so yes you have room for good or even optimal heuristics (if your infeasibility is lifted).
More good news is that looking at your problem this way i.e. slots to fill for your end result 'games' -which is your lowest dimension- probably makes the problem quite solvable. (If you looked at it from the all possible games perspective you would be looking at 65,889,460 possible games and their permutations/scheduling for your delay part)
Even more good news: your delay constraint is satisfied well by having each team wait the same amount rounds (minimum delay equals uniform delay - otherwise if a team waits less the wait is paid by another team maximizing the minimum delay) This gives us a fast heuristic - no need to run NP-hard exhastive solution on scheduleing/permutations.
Even better news: I am giving you a sort of heuristic to look at and solve this extremely fast! Looks like following this way you can get a lot of heuristics for your problem due to the large feasible space as outlined above so here is how you would go about it:
So first let's lift the infeasibility by increasing your maximum number of groups to 54. You can just have 42 if you like as your requirement with the same algo but the equal games will never work as aforementioned.
Now schedule your first 3 rounds (STEP=1) Groups 1 ...54 in a row meaning Game 1 is Team of Groups 1 2 and 3 vs 4 5 and 6, Game 2 is 7 6 and 8 vs 9 10 and 11 and so on until 54
Now for STEP=2 schedule your next 3 rounds (why 3 at a time? because 3 is uniform delay ensures min max delay per group -see note above)
Replace each Group by the Group + 3*Group modulo 55 so looking at them in a row your Round 4 becomes 4 8 and 12 vs 16 20 and 24 and so on. For example Group 1 will play with 52 and 5 against 9 13 and 17
Now for STEP=3 schedule your next 3 rounds
Replace each Group + 3 * Group modulo 55 again (using group numbers from the previous round)
For example your Round 7 has 16 32 and 48 vs 9 25 and 41 and Group 1 will play with 17 and 33 vs 49 10 and 26
Now for STEP=4 schedule your final 3 rounds (12 rounds scheduled after this step)
Do the same as above! So Round 10 has 9 18 and 27 vs 36 45 and 54.
Group 1 will play with 10 and 19 vs 28 37 and 46
Of course the above is a loop so you can have as many rounds/groups as you want (or your numbers allow)
Now for sanity check that your constrains are all met by the scheduling heuristic provided
(I only checked a few seems ok if not just change the modulo equation to include more variables STEP, Round, Game number etc - but again due to your large feasibility space this simple equation seems to also work, replace it just to get different schedules if you want more than one - although with one schedule you can schedule any tournament per note 2 below)
NOTE 1: I have the whole schedule here for now but it is probably too much to post.
NOTE 2: You can use the same schedule every time (just assign Group numbers to people and your new schedule is done each time)
NOTE 3: You seem to have room for even more groups or rounds if you want. To find out just continue the loop above until one of your constrains is not met.