I haven't heard about anyone else who have made use of three MT8870 like that.

You normally configure the components to control the filter time parameter for the chip, i.e. how long it requires to recognize a tone. 40ms is a quite common time for handling 70ms phone tones, giving 70ms safety margin. For special signalling I have been using them with much shorter filter times but then there must be no other sound on the lines or they will constantly false-detect.

The shorter filter time, the more false hits you will get from other noise on the line.

Having three MT8870 listening at the same time will not change their behaviour - if each one still have the same filter time then it really isn't meaningfull to poll them one-by-one every 15ms. You could just as well poll a single MT8870 every 15 ms. But better would be to poll much quicker or use interrupts.

I don't know where the DTMF tones comes from, but if you can better capture the timing then you can often make educated guesses. An automatic phone system may run 70/70ms timing and few persons are fast enough to press buttons faster. Common for phones is to produce 100ms DTMF tones or to produce tones exactly for the duration the button is pressed. So looking at the timing can help a lot. But have you made sure that you really "hear" silence between your two digits?