I don't monitor my heart rate routinely during a workout, but when I do it is easily in the 90-100% of my maximum. Having said that, I usually monitor it durnig a hard workout (fast 'hilly' run'), so no big surprise there. During a jog is about 70-80% of my maximum.
I would guess that a heathy diet and regular exercise are the key factor to 'train' your cardiovascular system.
I'm not medically trained but perhaps it is not unreasonable that lower levels of Hb call for higher heartbeat rates to compensate for reduced oxygen supply. But I would wait for more knowledgeable people to comment on that.
I'm also a beta carrier in my early 30's. My resting heartbeat is in the high 40's/low 50's.