XKB - remap greater/less keys into CTRL+AB08, CTRL+AB09

Question

I've recently acquired a new laptop with qwerty keyboard, which I intend to use as azerty (fr). Everything is fine except the LSGT key I'm missing, not present in this qwerty keyboard. Instead, I've decided to use keys AB08 and AB09 for that with CTRL modifier. This is what I tried in my symbols/fr:

key <AB08>   { [ semicolon,     period, horizconnector, multiply,    less ], type[Group1]= "LOCAL_EIGHT_LEVEL" };
key <AB09>   { [     colon,      slash, periodcentered, division,    greater ], type[Group1]= "LOCAL_EIGHT_LEVEL" };

Working well in term, except that it really doesn't play nicely with other applications (slack, postman...): it will usually trigger those applications keyboard-shortcut or such when I use AB08 and AB09, not only with less/greater but also with the remaining of the keys, like semicolon, slash, ... It essentially considers my newly edited AB08 and AB09 as containing CTRL

I've searched more but couldn't really find a solution. Ideally, I would like to keep the CTRL+AB08=less & CTRL+AB09=greater; but without disrupting other applications when using those keys. Could you assist me?