There are some unconventional methods, but the acceptance of the method shall be done after due design consideration and clearance and after checking with your safety officer (You may also check OSHA)
Fill the equipment with inert gas such as Helium or argon (With your solution in the tank). The pressure applied should be less than 1 Kg/Sq Cm. This pressure shall be decided by the designer. (Please note the FRP tanks are prone for damage even if the pressures is less )
If you are using He, then you may use sniffer, if you are using Air or N2 you may use Soap solution application from out side.
The second option is rather un conventional, this could also be a potential safety hazard. Here thin sheet of SS 316 can be mounted on to a holder and inserted in such a way that it touches the wall, then on the concurrent location outside apply High Voltage Spark test.
In both the methods the bottom portion cannot be checked.
What you may do is to check whether the peddestal on which the tank is mounted has any draining facility. (Generally the concrete floors are provided with drain ways for flat bottom tanks), if so, then seal the bottom ends with temporary sealent and pass low pressure He or Argon or N2 or Air from the drain way and observe for any bubble fom the top.
You may also check with some chemical engineer for some potential indicator solutions which would change in colour when it comes in contact with the solution in the tank, Then you may apply the indicator solution from out side and observe for locations where there is change in colour.
Also check with your NDT specialist whether you may use Dye penetrant check, whether the material is compatible for testing with DPT can be verified in a Mock piece with artificial defects the sensitivity may not be as great as you may see in a Metal, but i feel this DPT is worth a try, and additionally the procedure is very safe so long as water washable method is used. (Use of solvent washable is not preferred)
You may also apply Ultra violet Light (darken the area) from outside and check
The effectiveness of this method is not known.
Any way Good Luck and Please let know as to what you have done.