After some effort in deciphering your input, I can't see the point. You were in controlled airspace, weren't you? Isn't the tower controller in charge of her/his airspace, and responsible for all wright and all rong?
Jan, may I kindly suggest you do a re-read of air law? In virtually all controlled airspace that pre-PPL solo students encounter, VFR traffic is responsible for its own separation. That includes adjusting the circuit to suit other traffic. The exception to this would probably be a class B CTR, which is very rare in Europe, and even then ATC will expect you to act sensibly and not cut in front of other traffic.
Turning base at the "usual" point (wherever that is) and thereby cutting off traffic in front is a big no-no, both in controlled and uncontrolled airspace.
Option one - Continue further downwind before turning base. yep, I can see thats a good option. however, to play devils advocate, there is a danger of getting lost, especially for a second solo with presumably little knowledge of local area and none of nav. This would be the same if one was to fly away from the safety of "home" and the cct at this stage...how would you cope if you had not been taught PFLS (ok, so EFATOs probably have been taught by that stage). This course of action surely puts more stress on we Studes?
If there's just one aircraft ahead, surely you don't plan on extending downwind to outside the ATZ, or turn it into a cross-country? Anyway, there's always the option of orbiting on downwind (turn away from the runway please, so orbit over right with a left hand circuit) if significant spacing is required. Typically due to an IFR straight-in approach on final.
Another option is for the early solos at least not to go solo when the cct is busy or when ATC Is operating.
[My bold]
Seriously? You're not scared of ATC, are you? It's definitely something you have to get used to, but they are honestly there to help you, not to be a nuisance or danger to aircraft.
On the other hand, if you only flew with an instructor outside operating hours and never experienced ATC during your dual flights, your instructor should never have let you solo when ATC was operating.