To add to my previous comment, you own calculation is incorrect. Since you are under age 55 the combined total that can be contributed by you and your employer to your HSA for 2019 without using the last-month rule is $3,500 * 2/12 = $583.33. Even if you don't contribute through payroll deduction or directly, if your employer separately contributes $750 you will have $166.67 contributed under the last-month rule. Since you'll fail to meet the testing period, you'll owe a $17 extra tax with your 2020 tax return. The $166.67 contributed under the last-month rule will not be an excess contribution, so it makes sense to allow your employer to contribute that even though you'll pay the extra tax. Better to pay the $17 extra tax than to not get the $166.67 from your employer.
Also, you are not permitted to get the full $750 contribution by your employer and then obtain a return of contribution of $166.67 to avoid the $17 penalty because only amounts that are actually excess contributions are permitted to be returned in this way and the $166.67 is not an excess contribution as I mentioned above. (Even if you obtain this distribution and the HSA custodian reports it as a return of excess contribution, legally it would constitute a regular distribution, you would still own the $17 extra tax and, if you did not use the $166.67 for medical expenses, it would be subject to ordinary income tax and to a 20% early distribution penalty.)
