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I was told by every flight school I have contacted so far that I need to convert my UK PPL to a Canadian one..."
You'll need to manage your expectations with Canadian training organisations. Transport don't make this a requirement.
The 30 solo hours as part of the CPL training will be logged as PIC and these hours can be accumulated on a Canadian aeroplane using an FLVC or better. Any other hour building done as PIC on aeroplanes, whatever the state of registry, will count towards the total experience requirement, eg your existing 10 PIC hours done for the UK PPL count towards the 100 PIC hours needed for the Canadian CPL. When you make an application to Transport for the CPL, a copy of your personal flying logbook will be sufficient evidence of the total flight time iaw section 28 of the Aeronautics Act. However, Transport will require the aforementioned 30 hours to be recorded in a Canadian pilot training record. See this thread.
On a fine point, the FLVC isn't a conversion. You should be able to apply for second one. The bar against residents applying for an FLVC is made in subsection 401.07(1) of the regulations but it might not apply to persons admitted under a study permit. I don't know how Transport interprets this. As mentioned, if you need to do hour building and an FLVC isn't available, you could write the PSTAR exam (90% pass required), obtain a Canadian category 1 or 3 medical, meet the Canadian PPL flight experience requirements—read them because they go beyond the UK PPL requirements!—then apply for a restricted (foreign-based) PPL. The restricted PPL does not require a flight test. Re the FLVC, you should be able to pick it up at a TCCA licensing office a day or two after emailing copies of your foreign licence, medical, and recent logbook pages.
The PGWP is a one-shot deal and you must apply for it in a timely fashion. Any regularly scheduled academic breaks can be counted as study time for the purpose of extending the PGWP period, however, modular flight training courses usually won't be structured to include such breaks. You might be better off doing an academic course in another field, eg many universities have divisions of continuing studies where you can do non-credit courses that culminate in a diploma or certificate. Are you not eligible for a work permit under the IEC working holiday programme?
Jazz advertises a minimum of 500 hours. Westjet Encore advertises at least 750 hours. Actual requirements are probably higher but there's no regulatory basis in Canada for a minimum of 1 500 hours.