*On the student helpers issue... well, how long have you got?
The central admissions team don't recruit helpers for visit days, only open days. So, departments have to recruit their own helpers. We do pay but we're only allowed to pay in vouchers because the role is technically a 'volunteer' role to get around Visa issues.
We have a couple of helpers who are recruited at the start of the year who help us loads will various admissions events. They're recruited very professionally (applications, interviews etc.) but we didn't have that many applicants for these roles. I have no idea why. Anyway, when it comes to visit days, we need about six helpers to deal with the number of visitors so we have to recruit more people ad hoc.*
Who are they using for campus tours, widening participation events, visits from schools...? Without knowing which university it is that you're working for, it's impossible to know the structure of your various departments, but I would say it's unusual for the admissions office to be recruiting and managing student ambassadors. Have you checked if there's a separate student recruitment, or even widening participation team?
Only paying in vouchers is someone's administrative laziness. There's no reason why you couldn't either (a) open the role only to students on UK/EU passports, or (b) use the fact that Tier 4 visas allow students to work up to 20 hours per week in term time. Both RG universities that I've worked at used UK/EU and international students on their ambassador programmes with no visa related problems. I'm no lawyer, but having the vouchers also likely means that it's not legally volunteering anyway, and you need to pay minimum wage and have just as many visa issues www.gov.uk/volunteering/pay-and-expenses
The helpers you've recruited at the start of the year sound like the very basics of a workable ambassador scheme. When you readvertise, make sure you put out an email to all UG students, posters in the department, student facebook groups, tell students at the start of lectures (yourself and some willing colleagues!) and you could even do a refer-a-friend bonus to get existing helpers telling their friends about it. Every student should hear about the programme several times over! And convert some of the more capable (or potentially capable) ad hoc ones to be ongoing helpers.
Sort the pay issue out, advertise the helper scheme better (actually, rename it, helper sounds rather belittling) with the formal application forms, interviews, training and so on, and you'll have a passable group of ambassadors who can staff the events on a more reliable basis. Do it right and you'll give them experience that's worth putting on their CVs and will enhance their employability (and hence look better in the league tables...)