The biggest issue here is the disconnect in the salary range - is it a junior position or a senior position?

You want a PhD and would prefer experience. You would be better served to narrow the pay band and scope of the position in order to make sure you have a good alignment and not overpaying for the work - or underemploying somebody and they get bored and leave or are unhappy because you sold them a senior but the work is junior.

If it is an entry level position the pay is still on the end given a gov agency has no equity to offer. On the high end - that's what the cash portion of the comp would be at a normal company (you know this since you worked at Amazon) but not close to total comp.

Also working in IF for a gov agency isn't exciting to a lot of people so your candidate pool is already going to be tougher to dig through.