My first question is what is the age of your Model 1905? If it is indeed over a hundred years old, why do you feel the need for jacketed bullets? Pre-WWI revolvers were designed and built with lead bullets in mind. While jacketed bullets work in these vintage guns, pressures can be higher than lead given the same loading and weight bullet. This is an often debated issue, but being a long time reloader, I can say from experience that it is a lot harder to drive a lead core copper jacketed bullet through a bore than a lead bullet.
Steel strengths prior to WWI era were 30,000psi to 40,000psi, plenty strong enough for the standard 38 Special round pressures at or under SAAMI max of 17,500 psi. Today's steel is much higher tensile strengths, allowing for higher pressures and offering a larger safety factor.
As I understand things, there is a risk of shooting copper clad bullets at lower speeds, because the bullet may not expand enough to fill the grooves, sealing the bore, and can result in stuck bullets. Some reloading manuals used to state that potential issue, and so that may be a possible reason why you are having problems. In my opinion, these vintage revolvers have shot lead bullets from day one and shooters should consider doing the same moving forward. Also, at target load speeds, you should never see leading. I shoot my old M&Ps at 700 fps and they give remarkable results still today.