I'm afraid I'd fall asleep if I were to try something like this.

Which... I also think is fine? Sleep is a daily change of consciousness allowing for rest, recovery, reorganizing, etc.

Sleepiness is a very common challenge. A common mitigation is to find a way to sit comfortably without a chair back, forcing you to stay upright. I find it uncomfortable to sit cross legged for long stretches so I usually kneel with a large cushion under me like, kinda like a saddle.

Try stuff, see what works for you. Once you find a relaxed but upright position you may find you can sit for quite a while without dozing off.