Solid cores and RJ45 plugs are not designed to work together, yes I have tried, and it usually works, but it cannot be relied up. I long ago, swapped all mine over, to sockets, with fly leads. What happens is, the pin are inline with the wire, and tend to skid down the side of the insulation, and miss the copper. Using flexible, the pins can spear through the actual conductors. The socket IDC's, present a V, across the solid core, which nicks its way through the insulation.
I did once investigate if there were any RJ45 plugs, designed for solid cores and one seller claimed they stocked them. I bought some samples, they did seem to make slightly more reliable connection than the normal type, but not 100%.
Yep, I've done lots of stranded, into RJ45 plugs, it's not difficult. strip the outer, fan the wires out in the correct order, trim to length push in, crimp, then finally test with the continuity gadget. Once you start the fanned out wires going into the RJ45, they are retained in the correct order by the grooves in the plugs. Look through the clear plastic and if you see colour, white, colour, white all the way across, chances are - you got it right, if you fanned them out correctly at the beginning.