The payslips themselves are another report (actually a Form)

On ours we just have "Statutory Payment" which is an expression of:

CurrentPay.SAPPaid + CurrentPay.SPPPaid + CurrentPay.SPPAPaid + CurrentPay.ASPPPaid + CurrentPay.ASPPAPaid + CurrentPay.SMPPaid + CurrentPay.ShPPPaid+CurrentPay.SPBPPaid

as there isn't much room on payslips to list each one separately.  (Haven't fully checked, but it is likely that you can only have one of the payments above at a time (though within a pay period you may receive more than one), so with a bit of formatting it may be possible to overlay a description for each of the payments and have only the relevant one printed.)  When updated each different payment above goes to its correct location for the post update reports, etc.

You can check/change what is reported where by selecting your payslip (in the pre-update reports) and clicking [Edit].  You may find that your "Parental Leave" is an expression containing something like ours above.  Similarly for the historic (reprinting) payslips, except that for this we have an expression of 

Updates.SAPPaid + Updates.SPPPaid + Updates.ASPPPaid + Updates.SMPPaid + Updates.ShPPPaid+Updates.SPBPPaid

(Which I notice actually misses two out compared with the current: SPPAP & ASPPAP, but as we've only had Shared Parental and Maternity pay it hasn't affected us [yet] on a payslip reprint.)

re reclaiming.  I think (check with HMRC) that when you send the EPS to claim it, HMRC receives a cumulative value of the SMP reclaimed so far.

One further thing to note is that Sage calculates statutory payments to the process date.  This caught us out as we process our payroll a couple of weeks before the end of the month and pay them about 10 days before the end of the month, but pay for the whole month.  (I only took over the payroll recently and everyone is used to their payslips showing the process date as the date they actually get paid even though they are being paid for about 10 days after this.)