Right now they seem to be bit weak
1) Don't judge the garden light performance by what you see in winter.
I did some testing on a solar garden light in January here in Melbourne and at midday under the direct summer sun the charging rate was 26 mA. Today under bright overcast conditions in winter the Sun was behind a white cloud and very bright to look at directly. The garden light is only getting indirect lighting in these conditions and the charging rate was only 2mA.
This particular garden light runs the LED at between 9 and 8 mA so on overcast days in winter the battery is only going to charge up enough to run the LED for a couple of hours each night.
The size of the battery is not going to make any difference to the performance during these overcast days.
[EDIT] 12pm Monday Melbourne is full overcast. The charging current for the same garden light under these conditions was only 6.4uA.
Would it be OK to put some 1800mAh NiMh low self-discharge batteries or it makes no sense?
2) You can test your own garden light to see what you can expect with an AA battery during summer. You may not need to go the trouble of adding Li-ion cells or multiple AA batteries. You may find you will get enough from a single large capacity AA.
I have an Arlec Trillium garden light that uses a single AA battery that I did a different test on. I charged a 1000 mAh battery fully, put it into the garden light, turned it on and put it upside down on a table. This blocks all light to the solar cell so the LED is on 100% of the time.
Date Battery voltage LED brightness
Wed 01:30am 1.365V Very bright (uncomfortable to look at directly)
Wed 11:45am 1.301V Very bright
Wed 09:30pm 1.292V Very bright
Thur 01:30am 1.290V Very bright
Thur 09:30am 1.287V Very bright
Thur 09:30pm 1.286V Very bright
Fri 03:50pm 1.279V Very bright
Sat 00:30am 1.272V Very bright
Sat 01:00pm 1.252V Bright
Sun 02:11am 0.807V Dull
I replaced some 600mA NiCad batteries in my garden lights
3) Check the capacity of cheap AA batteries, don't trust the marking. I have some batteries that came with one of the garden lights I have and which are marked 600 mAh but when tested on my charger only take 270 - 330 mAh.