While approaching to land, you are on the backside of the power curve, so pitch for airspeed, power for altitude. You have correctly indicated about managing airspeed. But it is not as difficult as it sounds. If you were flying at the beginning of the slip, you will continue flying through the slip unless you mess with nose positioning, or pitch. TL'DR, DON'T PULL UP while you are in cross control.

Here are some suggestions. As one of the child comment stated, go fly a glider for a few hours. It will immensely help with flying "not straight". I started it for gaining better understanding of flight but ended up finishing a commercial ticket on glider as well, because I enjoyed it so much and also just for the bragging rights.

Secondly, cross control is perfectly safe till the time you pull back on the stick. That is how you get into cross control stalls, the starting configuration for a spin. When you are slipping, you should actively trim nose down, (that you should have done already, remember you are approaching to land), and maintain just a little forward pressure as you fly sideways. I would recommend, grab a competent CFI and get cross control stalls nailed. I know it is not a part of PPL, something I am very pissed about. Hell, PPL in US does not even need spin training. Bollocks, if you ask me....