If the gates have time restrictions at Forest Hill for off peak, this will have problems for people trying to give themselves lots of time to get over the bridge
This is true. TfL's website is not very clear about this, but it would appear that you cannot go past the gate until the allotted time:
Tfl wrote:
When using Oyster to pay as you go on Tube, DLR and London Overground services, higher Oyster fares apply Monday to Friday from 0700 and before 1900. Lower Oyster fares apply at all other times.
Please note that the fare charged is determined by the time at which you touch your card on the yellow reader at the start of your journey. For example if you plan to catch a train that leaves Euston after 1900, but you touch in before 1900, you will be charged the higher Oyster fare.
Although it looks like there are now four minutes' grace in the evening (not sure about the morning...) That report doesn't say anything about Travelcard peak/off-peak which applies to the Oyster daily capping, but I'd assume that the same applies.
TfL wrote:
If you use Oyster to pay as you go on the Tube, DLR, London Overground and some National Rail services, the system will look at your journeys in a 24 hour period (from 0430 and before 0430 the next day) and the amount you pay will be less than the price of an equivalent Day Travelcard. If you also use buses or trams during this period these trips will be included in this price cap. Our aim is to ensure that Oyster always charges the lowest fare. Where it doesn?t we will refund the difference.
TfL wrote:
Day Travelcards (Off-Peak)
Can be used from 0930 Mondays to Fridays, all day Saturdays, Sundays and public holidays, on the day of validity and for any journey that starts before 0430 on the following day.
Reading between the lines you will be have to call them to dispute the charge each time (at 3.5p/minute)....