Use hydraulic clamp fixture, same resin, fix o-ring on the plastic injection mold tooling plates, fix pillar on injection molding machine plate. Assemble cooling outlet(4 pairs 1inch for fix and move sides) and quick oil connects. You can got 25 minutes change over time with no big pressure and very low investment. That is exactly what I mean. please check the fitting between the bush and the tie bar, and furthermore maybe the clamping system of your moving plate. normally it should be the issue of the hinge.

Possibly press, but check your interlocks on as mentioned. If they are worn, cores shift. Hopefully it is a well built mold with not only leader pins and PL locks, but interlocked cores and cavities as well.
This can be a tough problem to solve at times and high maintenance. check the wall thickness in bottom of container. these should be a bit thicker than side wall. also test by turning off heats to one drop and see how fills, than switch to other cavity, how does that fill. I have run into this as you mentioned older tools, how many times was the PL cleaned (ground) and how often was the core shifted. Further can run short shots, run from a fast fill to slow fill and since short watch fill pattern this may give optimum fill speed.

2 other things... clamp injection mold up and shoot an air shot how much pressure, make short shot 90% full how much pressure make short shot 10mm diameter how much pressure... this well show where pressure is lost. do for each indiviadual cavity and may find out something... you do subtraction of pressure as fills... poor mans mold flow.