Years ago we supplied a stencil where they put an eutectic cap on the high-lead balls. The stencil had small domes (3 mils deep) etched into a thick coupon.

63/37 Solder Paste was doctor bladed into the 3 mil pockets. The FC was placed on the coupon with the bumps registered to the pockets. The FC and coupon were then sent through reflow forming an eutectic cap. The stencil was rendered non-solder wetting by coating with Chrome.

With the data that you have presented it is not clear what the route cause of your problem is. It could be either the activity of the flux (wrong type of activity or insufficient) or it could be profile related - it is not clear.

If it is a profile issue with there being insufficient time for the molten solder to form any appreciable intermetallic bond to the solder bump. If this is the case then additional heat and time should improve the situation. Also check the O2 content in the oven if this is to high this could result in flux exhaustion.

This can lead to "graping" where the surface of the solder looks like a bunch of grape with the outline of individual solder spheres still visible in the surface of the solder fillet and poor wetting. It is desirable to use the largest solder powder size that you can. This gives the least amount of solder surface to oxidize and reduces the load on the flux. It may be worth considering a larger particle size if possible.

Soldering to high lead bumps can be a big problem. First how are the bumps formed? They could be heavily oxidized this would cause the issue. Also you say you are using an aggressive flux. This may not be compatible with the high lead.

Just because a flux is deemed aggressive it does not necessarily mean it is the proper match for a high lead bump. Dwell time and time to reflow are critical. The faster you get to reflow the better fluxing action you will achieve. Also on high lead bumps run hotter I would recommend a 235C reflow spike temperature.