Add multiple Date Dif together to get total length of service, if date blank, use TODAY

I use excel to track hire and term dates of employees. My line of work is seasonal so employees get termed and rehired on a regular. Column C is the first hire date, D first term, E second hire date, F second term date and so on.

With this setup, I want to calculate the total amount of time a person has worked here in years, months and days. So I need to calculate the date difference between F and E and the difference between D and C, then add those differences together.
I started with this as my base formula (it's since grown to include up to 5 hire and 5 term columns):
=DATEDIF(C2,C2+((F2-E2)+(D2-C2)),"Y")&" Y "&DATEDIF(C2,C2+((F2-E2)+(D2-C2)),"YM")&" M "&DATEDIF(C2,C2+((F2-E2)+(D2-C2)),"MD")&" D "

And this works well except that some people have never been terminated, while some have been hired and termed 5 times or more so there are empty cells all over the place. I needed to tell the formula that, if a date cell is blank, use today's date. This is what I came up with:

=DATEDIF(C2,C2+((IF(F2,F2,TODAY())-IF(E2,E2,TODAY()))+(IF(D2,D2,TODAY())-IF(C2,C2,TODAY()))),"Y")&" Y "&DATEDIF(C2,C2+((IF(F2,F2,TODAY())-IF(E2,E2,TODAY()))+(IF(D2,D2,TODAY())-IF(C2,C2,TODAY()))),"YM")&" M "&DATEDIF(C2,C2+((IF(F2,F2,TODAY())-IF(E2,E2,TODAY()))+(IF(D2,D2,TODAY())-IF(C2,C2,TODAY()))),"MD")&" D "

It works for most of my employees but not others and I cannot find a rhyme or reason.

I've tried making sure my columns are appropriately date formatted and I've gone so far as to try and restart from scratch but nothing I do makes the calculation work consistently. I'll have two employees who have been hired/termed the same number of times and the formula works for one and not the other.

Any ideas? I've attached a redacted copy of my spreadsheet for reference.

Part of your problem is that many of what appear to be dates are actually text.

So you first need to convert all the date cells to actual dates.

You can detect the problem cells by trying to change the formatting style, you will see that many will remain the same, and they are the ones that are text.

Another problem is that there are records where the termination is AFTER their rehire date... cell D2 is an obvious example

Changing the format style (eg, from 03/25/2019 to 2019-03-25) will only allow you to detect (see) potential issues, but it wont correct them.

To convert all dates to the same format:

1. insert two columns after each date column, for example add two columns after column C.
2. put this formula into (new column D) cell D2 and drag down:

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3. Put this formula into (new column E) cell E2 and drag down:

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4. select column E
5. right click and choose "Copy"
6. right click on column C
7. choose Paste Special > Values
now all the dates in column C are the same format

WARNING!
because the formatting of the cells is not originally consistent, some dates may switch the month and days (its happening as i type this)

i would normally have done this to completion and provided the file with dates converted, but as there are so many dates that are not "behaving" with the conversion i am reluctant to provide a file where the data has corrupted (new dates are not appearing the same as old dates) from original.