Your charge voltage is way too low. Printed on the side of most SLAs is "Cycle Charge at 14.7V, Float at 13.7V". It will take forever to reach even 60% charge at 13.5V.
You need a current-limited full-wave rectified output wall-wart which has an open-circuit voltage of 15 to 18V, but is current-limited to less than 0.5A (more like a constant-current supply, less like a voltage-regulated supply). A trick that works for me is to find the Wall-Wart with the right output voltage, and then connect a 24V 10W lamp in-series with the 120V input side of the wall wart (I break open the plastic case of the wall-wart, and repackage it into my own enclosure). The lamp acts as a "ballast", or crude current regulator. The non-linear filament resistance is what accomplishes that.
I use the A/D inside the PIC to monitor the battery voltage. When the battery needs charging, the charging cycle consists of turning on a high-side PFET switch which connects the wall-wart output to the battery positive pole. Since the wall-wart is current limited, the PFET is just a switch, fully on or fully off, so dissipates almost nothing. (Heatsinking not required).
The PIC watches the battery terminal voltage during charging. When the battery voltage reaches 14.7V, it keeps the charger on another 15min (regardless of how high the voltage climbs during that 15min period), and then switches off the PFET.
The PIC continues watching the battery voltage, and turns the charger back on if the battery voltage sags below 13.3V. This time, the charger turns off upon reaching 13.8V. This cycle repeats until the battery is removed. When the battery is disconnected/re-connected, the PIC goes thru the initial charge cycle again, including charging for 15min past reaching 14.7V.
If you are in a 240V country, you may have to find a different lamp to use as a ballast ahead of the wall-wart. Maybe a 120V lamp (if you can find one)? You know you have a lamp with the right filament resistance when it glows about half brightness early in the charge cycle, and then glows very dim toward the end of the charge cycle.