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Maybe the solution is easier. Go to your Akeeba Backup Configuration page and use the following settings:
- Minimum execution time: 1 second
- Maximum execution time: 7 seconds
- Runtime bias: 75%

And, yes, please do check your free space. Last time I checked hard drives had a finite (not infinite) capacity and it costs about 65 cents per Gigabyte (half if you use consumer-grade hard drives which crash all the time, three times as much if you are also taking backups). I don't think any host would offer truly unlimited capacity without charging you extra; they'd be out of business very fast. What I have seen is that hosts with "unlimited" or very generous (100Gb or more) plans give you a token amount of disk space, e.g. 1Gb. When you have used it up you can ask them for more and it's up to them to give the extra space to you.

I have a suspicion... Go to the Configuration page, click the "Configure" button next to the Archiver Engine and set the part size for split archives to 10Mb or, if that doesn't help, 5Mb. Any joy now?

Awesome! You can always try different (higher) settings until you see how high you can go before the backup fails. This is entirely host-dependent and never written in the host's documentation :)