PHP/Ubuntu: Intense background tasks - sepreate server, or bigger single server

I manage a Ubuntu 16 server (running a public website), on AWS EC2 infrastructure.

The site has a number of fairly intense, and regular background tasks (via cron) to do, and it's running the risk of overloading current resources and therefore affecting end users / public.

The database is hosted on AWS RDS.

I'm unsure whether to:

1. Simply increase the resources available on the single EC2 (it's currently a t2.small, so really very little resources)
2. Launch a separate server, solely for the background tasks, so any lag a background task may cause on the server won't affect end-users (the database is on RDS so would be a pretty easy setup)

I thought about setting up AWS Load Balancing and Auto Scaling but came across two issues:

1. Scaling can take 60 seconds plus, so the end-users will still experience potential lag
2. All servers in the autoscaling group will be the same, therefore all running their own instances of the regular background tasks, resulting in potential double-ups, and more importantly, each server won't be better off as each is still doing what a single is asked of.

I am leaning towards a separate server for the tasks, as it means if that falls over (or lags), end-users aren't affected at all, and it seems a 'tidy' option, but is a bit more admin and setup. Cost of having a second server isn't an issue.

So my question is really, what do you think is best, and why? And am I missing a better idea?

(NB improving the efficiency of the background tasks isn't an option!)

Thanks in advance Rob