Have you tried piranha solution? Is cheap, it does not attack quartz and removes metals and organic material. It is prepared 50:50 H2SO4, H2O2. Prepared in small quantities is safe to use, considering you have to collect spills with zeolite or another inorganic absorbent, not organic and never paper and considering it heats a lot.
You could use aqua regia, It´s the best option to clean withouth damaging the quartz. The mixture is formed by mixing concentrated nitric acid and hydrochloric acid, you can use it in 50/50.
The sure shot option is hot "Chromic acid". We use it daily...so go for it.
Dissolve a arbitrary amount of K2Cr2O7 in water as a saturated solution. Little over saturation is also fine. Pour (98%) H2SO4 with the help of a glass rod. Be very careful for this step as it produces a hell lot of heat and may cause accidents.
After addition you will find a reddish-orange solution. Pour it in the cuvette up to its neck while hot and keep for 2-3 hours.
Discard the solution. wash the cuvette with lq. soap and clean by water repeatedly.
You may also use 80 % H2SO4 . Pour the acid into the cuvette and add carefully 30 % H2O2 from pipette. Be careful due to exothermic decomposition of peroxide. After total decompsition of peroxide, wash the cuvette with distilled water and then with ethanol p. a, and dry at 80 oC.
Also, a 65 % HNO3 might be tried. After a few min. after filling cuvette with the acid expose it to supersound. Prior to cleaning the quarz cuvette, test the effect of supersound generator on an ordinary glass cuvette.To avoit corrosion of the generator put cuvette with HNO3 into glass test tube filled with distilled water. The level of water after immersion of cuvette should not be higher then top of the cuvette.