If you can persuade existing card issuers to increase your limit that will increase your available credit and therefore reduce your credit utilization, which increase your credit score. .... Just make sure that the card issuer doesn't pull a formal credit report before doing doing so. Otherwise sitting tight might be all you need to do and your card issuers may just jack up your credit limit (again) without you needing to ask.

Six years of history and lack of history still dings me, albeit slightly.

I've actually found it quite easy to build credit.

Arrived in June 2017 and immediately was given a $2,000 unsecured credit card that I used to purchase everything and pay off immediately.

In October I was approved for finance on a new car by Jaguar.

Then this month I've just been approved for a mortgage and the rates I've been offered are based entirely on my score which is quite good, so no penalisation for lack of history.