Sounds like your tuning issues weren't fully addressed, which can be difficult at best. After tuning my bow, which admittedly took a while, my single bevels don't steer the front end of my arrows, they fly great! My heavy arrows are also not affected near as much in wind as my hunting buddies who still shoot "darts".
I've noticed Broadheads "steering" arrows only happens if shafts aren't spined correctly, broadheads aren't mounted straight, or your bow isn't completly tuned to a specific arrow & broadhead setup.
As others have shared in the past, I too have seen way too many lost elk shot with fast darts over the years, both fixed blades & expanding. At the same time, I've seen none with heavy setups. And yes, every animal or situation is different, & many fast darts are quick kills, but on average, I'd argue fast darts have accounted for more losses by far than heavy setups, on average, for a variety of reasons.
Below is from a unit 8 bull a few years ago taken at 35 yds with a single bevel broadhead, complete pass-through, with sheared ribs on both sides. Notice the "L" cut, typical with rotating single bevel heads as they pass through tissue.
This heart-shot bull went about 100 yds in a matter of seconds before piling up. Also note the broadhead was still "shaving sharp" even after taking this animal.
For the reasons above, on elk, I'll be using my heavy arrows & single bevel broadheads. Note that on deer etc, I too shoot "fast darts".