Air Carrier Captain reported correction on unstable approach resulted in an ATC altitude alert and a CFTT event.

Narrative

Pilot Flying on a Visual Approach backed up by the LDA Y for DCA 19. Me and the FO briefed the LDA Y for runway 19 in DCA. Due to weather at the IAF ATC gave us a base to final turn at 2100 feet maybe 1-2 miles behind the final approach fix. Meanwhile they also requested us to keep our speed up because; 'we were #1'. ATC asked if we had the river (which we did) and so I proceeded to click the autopilot off and hand fly. I realized that we were going to be high so I started a decent down to be abeam the bridge (900 ft) as the visual approach chart depicted. Our decent rate between the final approach fix and the VDP was between 1.0-1.6 vs down. Before reaching our briefed minimum I began to arrest the decent rate to no more that 1.0 down. During this time ATC issued a Low Altitude Alert and told us to check our altitude. At Key Bridge we were at .8 VSI at 1100 ft and stable and continued. I didn't feel comfortable with using the autopilot on such short notice with an 'irregular' approach setup which might be fine but I should have had a better 'big picture' on what to expect from myself when shooting the approach.