Rollovers are limited to rolling over only one distribution in any 12-month period, so only one of the distributions made in the last 60 days is permitted to be rolled over.
Instead of doing a rollover, you might be able to get the HSA to accept a return of mistaken distribution, although I'm not sure if this qualifies as a mistaken distribution. A mistaken distribution is one where "the account beneficiary reasonably, but mistakenly, believed that an expense was a qualified medical expense and was reimbursed for that expense from the HSA." I don't know if not understanding the law and getting incorrect information from the former employer is "reasonable" cause. It's up to the HSA administrator to make that determination. Also, the HSA is not required to accept a return of mistaken distribution even if you have reasonable cause. HSAs are generally more likely to accept returns of mistaken distributions if done in the same year as the distribution since they will not have to issue any corrected Form 1099-R to reduce the amount of distributions reported on an original Form 1099-R.
Also, the distributions can be used to cover any qualified medical expenses incurred after the establishment of the HSA, so you might have past medical expenses beyond the $1,000 you mentioned to which you can apply these distributions.
