Electrical – Butterworth bandpass – higher roll-off than expected

It is possible with an IIR filter, but not accurately with a plain Butterworth filter. As far as I can recall, the only IIR filter with flat group delay is the Bessel, whose stopband attenuation is inferior to the Butterworth.

The problem with the Butterworth is that the group delay is a function of frequency, therefore the different frequency components of your peaks are delayed by different times.

One solution is to follow the Butterworth filter with a "group delay equaliser" consisting of approximately as many "all pass" stages as the filter itself. This will give you a good approximation to a constant group delay. I wouldn't presume to advise you on actually designing the equaliser.

All in all, I think the FIR filter is a far simpler approach, as well as more accurate : I don't know why you regard its delay as "approximate".

The LM358 and LM741 do not have enough bandwidth to do what you want. At 200kHz the LM358 can only manage about 10dB of gain. It also has poor slew rate and a high phase shift at this frequency, resulting in bad filter performance and distorted output.

If you don't have access to better opamps then you will have to use 'passive' filtering. Conventional IF amplifiers use a tuned transformer between each stage, with a tapped primary and loosely coupled secondary to achieve high Q. The downside of high Q is narrow bandwidth, but by staggering the center frequency of each stage the overall bandwidth can be improved without compromising stop-band attenuation.

You could build your own transformers from scratch, but it might be easier to scavenge some from an old AM radio and modify them to suit (you might even be able to leave them on the PCB and use the entire IF circuit as is). Inside each transformer you should see a small capacitor in parallel with the primary winding, which creates the tuned circuit. Wiring another capacitor across this will lower the frequency. To get from 455kHz to 200kHz you need to add about 4 times more capacitance (might be 2~10nF, depending on the value of the original capacitor).

The circuit below shows the IF part of a typical transistor radio. I have highlighted the capacitors that are in each IF transformer. The transformers are often coded with a color to indicate what stage they are in:- yellow = 1st, white = 2nd, black = third.