As stated by Richard & Paul, most lead-acids such as car batteries and SLAB's can float high after charging and be a disappointment in terms of capacity, when you try to draw current because they are rated at what's called the '20-hour rate.' (Except aircraft batteries which are rated at the 1-hour rate).
In the case of your 7Ah SLAB, a new unit is specified to supply 7Ah only when it is discharged over a period of 20 hours which is in this case a .35 Amp load. (The 20-hours is in small print or omitted altogether - a bit like dBi and dBd for antennas.) As the current is increased, the total energy which can be extracted decreases quite markedly.
If you were to select a specific load (in this case 3.9 Amps) which would discharge the lead-acid (to 10.8V) in just one hour you would have to derate it by a factor of .559 and your 7 Ah then becomes a 3.9 Ah one. (See table).
They are more forgiving of ill treatment than the pernickety lipo's however as I can readily testify just lately after testing my full compliment of the latter with similar and in some cases much worse results than yours. I have had to buy four more 5Ah ones and one of those has swelled after only one month and its capacity reduced to 60% of its capacity on receipt. It's had just one SOTA.
I am trying my best to treat my lipo's better. Longer term storage should not be at full charge - some say 50%, others 70% etc. If you charge in the house you should not then store in a cold shed and vice versa. About 3.3 V/ cell is the bottom limit of discharge but some say a bit less than that but you should (or likely already have) check this out for yourself.
My IC706-2G shuts down at 9.6 V but my FT817 can still be 'annoying' an external 11.1V (3-cell) nom li-po at 7.2 V!!. That will take it down to 2.4 V/ cell, well below the danger level where it is likely to be destroyed. I have had to add a power-line diode chain (3 x 1N5404's in series) to help mitigate against this possibility.
Below is a Varta battery table which shows how 20-hour rated lead-acids are derated as a function of discharge time. It's what I used for aircraft and submersible batteries in a bygone age when I used to work. The graph below is plotted from the values given.
Good luck with the activation but be prepared to sweat that little bit more!
Above: 20-hour rated lead-acid battery derating factors for shorter discharge durations.