Lately, I've been approaching 'basic' irrational beat divisions in a certain way which has been of some help. What I do is subtract the 2nd number from the first and then put the remainder in a fraction as the numerator and the 2nd number in the original ratio as the denominator. For example: 4:3 would be 4-3=1 and then 1/3. I then add this fraction to every original division of the beat. This shows me how the original division fits into the irrational one (in this example, the old division is equivalent to 1 and 1/3 of the new beat division). Of course, something like 4:3 can be more easily 'felt', but this approach could be extended to more complex irrational divisions. The obvious weakness to this approach is that it's a bit imprecise: you would need to have a feeling for how much time the beat occupies since the new division would be more important for calculating specific durations.
After working out rhythms in this way, it has made me wonder if using 'wrong' ratios (smaller #: larger #) would be more effective, since the original division would be remain prominent when calculating durations. For example: if we were working with 3 8th notes in the time of 5, each of the 3 8th notes would be equivalent to 1 and 2/3rds the length of the old 8th note value.