I'm 64 and considering filing for reduced benefits now. If I do this, would I be able to use the stop, restart strategy down the road in order to collect full benefits at FRA?
No. If you start drawing benefits prior to full retirement age (FRA), you can't voluntarily suspend your benefits until you reach FRA. And, your benefit rate will be permanently reduced for any months that you are paid benefits prior to your full retirement age (FRA). Your benefits could be involuntarily suspended prior to FRA if you work and earn too much (https://www.ssa.gov/benefits/retirement/planner/whileworking.html), but you wouldn't be able to pick and choose when to stop and start your benefits until you reach FRA.
The start-stop-restart strategy is normally used to describe starting benefits prior to FRA, then voluntarily stopping them at FRA, and then restarting them at age 70. That can sometimes be an advantageous strategy for people with a spouse or child(ren) who are eligible to receive auxiliary benefits on the worker's record. However, the potential advantages of that strategy were hindered in many cases by the Social Security amendments that were passed by Congress in 2015. That legislation mandated that auxiliary benefits payable on a worker's record can't be paid for any months that the worker voluntarily suspends their benefits (https://www.ssa.gov/benefits/retirement/planner/claiming.html).
Suffice to say that if you collect any Social Security retirement benefits prior to FRA, you'll permanently retain the applicable reduction for age that's assessed to your benefit rate. You could still voluntarily suspend your benefits between FRA and age 70 in order to accrue delayed retirement credits (DRC), though. DRCs increase a person's Social Security retirement benefit rate by 2/3rds of 1% for each month that they don't collect benefits between FRA and age 70, but that percentage increase would be applied to your reduced benefit rate if you start drawing benefits prior to FRA.
It sounds like you should strongly consider using our software (https://maximizemysocialsecurity.com/purchase) to fully analyze the options available to you so that you can determine your best strategy for maximizing your benefits.