Bit evasion, respect issues under saddle

Hi! I am looking for some info on how to fix my new horse. Hes a 15 yr old welsh cob gelding. He was used in kids camps and ridden english for the last few years. This year he didnt go to camp because he got too strong in the bit for the kids to control. He is a fast mover. Very quick on his turns. The problem im having is that when riding him, he pokes his nose out and raises his head when you try to rein him at all. He does much better when neck reined on a loose rein but he will still do this. He will also just suddenly take off with a burst of speed as if trying to run away from the bit. hes hard to get stopped and then wont stand once he is stopped. My friend is riding him in a bitless bridle but he still has issues. I assume hes just gotten soured on riding because of the kids and has learned how to evade the bit. He also gets irked when he gets fussed over during grooming. He has tried to nip me a few times, which shows some respect issues. He will lunge good for me and stand to be mounted and he hasnt bucked but he acts like he might. He is also high headed due to having a really short neck. What can i do to get him riding like i know he used to? Im using a broken curb bit. It is a modified tom thumb with a copper roller in the middle and short shanks. I tried a regular snaffle but he just bulls into it too much. I tried a low port solid mouthpiece curb bit but that really made him fight me. Should i try a hackamore? Ive had his teeth checked and there are no sharp ones.