How are the gain and corner frequencies calculated for this speech bandpass filter

The "Dual Decompensated" in the IC's title is biting you.

Two things come to mind. The description in the data sheet mentions that that IC is stable in gains of 10 and more, and you are low gain.

Also

From the data sheet: High Speed Operation When the feedback around the op amp is resistive (RF), a pole will be created with RF, the source resistance and capacitance (RS, CS), and the amplifier input capacitance (CIN ≈ 2pF). In low closed loop gain configurations and with RS and RF in the kilohm range, this pole can create excess phase shift and even oscillation. A small capacitor (CF) in parallel with RF eliminates this problem. With RS (CS + CIN) = RFCF, the effect of the feedback pole is completely removed.

Even though you have no resistor in your feedback path, maybe R2 is working its way in somehow. You might try a small cap in parallel with R2, but be careful of your frequency response. You could also try a different configuration filter.

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.