I did stuff like prop blankets around his head so he could sleep in the front-facing carry at this age.
Another trick I use when he's overtired is,
I put on loud music, hold him very tight, and dance, walk, bounce *vigorously*. I support his head really well and just practically jump up and down. I can walk in a circle downstairs, or I walk around the perimeter of a room, in circles. I've found that he goes to sleep easier if I walk in circles in a small area, I guess because it's boring, rather than take a long walk outside, where the interesting sights keep him awake.
Once he's asleep, if my goal is for him to catch up on sleep, I would just hold him and nurse him back whenever necessary until he had a solid amount of sleep. I might devote several hours to this for a few days if possible... Once he's 'caught up' then sleep becomes easier again [sometimes].
It won't last forever.
This too shall pass. [and then probably happen again, and then be over again, and then happen again.]