How to sumif values (days worked) to each month, across a range of multiple weeks

I'm trying to extract the days worked in particular months, across entries in weeks which are divided into columns. The current formula I have works well in that it allocates full days correctly, although it ignores all decimals. For example an entry of 3.5 days allocated to the week commencing 31st May would allocate 1 day correctly to May, but 2 days incorrectly instead of 2.5 days to June. Any tweaks or other solutions would be really recommended!! Happy to commission someone if it becomes more involved. Many thanks, Matt.