It is important you spread all that real ‘PageRank’ – or link equity – to your sales keyword / phrase rich sales pages, and as much remains to the rest of the site pages, so Google does not ‘demote’ pages into oblivion –  or ‘supplemental results’ as we old timers knew them back in the day. Again – this is slightly old school – but it gets me by, even today.
Hi Kai! Using synonyms now and then is a great idea. It definitely makes your copy more natural and pleasant to read. And Google will comprehend that you’re talking about the same topic. You might want to use the keyword you’d like to rank for a bit more often than just once or twice, but don’t fret to use synonyms now and then. We’re not able to detect them with our tool yet, though.
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.