MusclePower do sympathise - I spent 20 years not being able to go properly. Not saying what I had to stick where though! I had a rectocle repair, but that has not solved all the problems and I have had to embark on a long program of trying to get diet, laxatives etc right so that it does not recurr.
I know that before a period, the oestrogen is goes lower, and the progesterone stays higher. Just before, it drops and the period starts. Progesterone slows down smooth muscle (the muscles you have no control over, like your intestines).
The progesterone slows down the peristalsis in the intestines and food takes longer to get through (you can test this with sweet corn -I never saw it again!). As well as drier and harder stools, caused by the slow passage throught the colon, where water is removed, they just do not want to come out. Could it be that your intestines are moving more slowly and you are not getting any 'push' from your rectum?
Fybogel is brilliant if you do not have enough fibre in your diet, but if you do not drink enough, or your intestines are slow, it dries out, as the fluid is taken out in the colon, and helps bung/slow things down. The same is true of things like all bran. This is why soluble fibre is recommended these days. It might be worth keeping a bottle of water handy in the days leading up to your period and so that you never feel in the least bit thirsty.
I saw a physiotherapist who specialised in pooing (who knew there were such people!) who recommended coffee for increasing peristalsis. She said that you should stick to regular meals, as this encourages the peristalsis, which starts at the top and works its way down, like a wave. For this reason, it is best to go to the loo after a meal.
I hope there is something here that will help you. The kiwi fruit was a really good discovery as I found it helped the 'push' as well as the softening, but you can tire of them (retires to eat another bloody kiwi fruit)
(As for the incontinence, there are oestrogen receptors around the urethra, as well as in the vagina. When the oestrogen levels drop, it plays havoc with that area - makes urge incontinence worse too.)