What can a Reservist do to not have to wait to become eligible for promotion after signing a rank waiver?

While your husband was able to make SPC while in the Reserves and keep it when going Active Duty, what is presently happening is that when your husband went Active Duty as a SPC, his Date of Rank was recalculated to a date where he would NOT immediately face the RCP (Retention Control Program) where he would be removed from Service as a 10 year SPC. What this basically means is that your husbands Date of Rank put him at a spot where his Active Duty Time in Grade does not meet the requirements to be promoted to Sergeant as of yet.

Promotion to E-5 has a primary zone requirement of 34 months Time in Service (TIS) and 10 months Time in Grade (TIG).

When your husband transferred to the active component, his TIS changed. The TIS for a reserve component Soldier is calculated from when they joined the military (their Pay Entry Base Date). In the active component, it is calculated from their Basic Active Service Date (BASD). For simplicity’s sake, think of the BASD as the day he enlisted in the active component and then back it up by how many days of active duty he’s had before that.

For example, if his basic training and AIT were eight months total and he had no additional active duty time, then his BASD would be eight months prior to his enlistment date.

Now that the confusing stuff is out of the way, back to his eligibility. From the timelines you gave, it sounds like he had 10 months of active duty time prior to enlisting in the active component. Those 10 months + 14 months of active duty currently + 10 months he’ll have to wait to be eligible = 34 months (the TIS requirement for promotion to E5).

So, is there anything he can do to get promoted earlier? Yes… Impress his unit commander so much that they would recommend him for early promotion. The eligibility for ‘early’ promotion (called secondary zone) is 16 months TIS and 4 months TIG, so his unit commander could put him in now (theoretically). However, that is a very subjective evaluation by his unit commander and frankly only ‘rock stars’ get put in for early promotion.

My advice to him is to concentrate on ensuring his Distributed Leader Course Level I is completed, that he’s met any other requirements that might be required of his MOS, and that he starts maximizing his promotion points – especially the ones from the ACFT and his weapons qualification.
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AR 600-8-19 (Enlisted Promotions and Demotions) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN36067-AR_600-8-19-000-WEB-1.pdf