To remove an unnatural (inbound) links penalty, you'd have to remove the majority of links Google sees as unnatural and disavow the remeining ones you can't remove. The links causing these manual actions aren't the spammy, automated ones (those are covered by algorithms like Penguin), but either paid links or PBN links. There are two scenarios:
1. You run a very established site with loads of great, naturally grown links, a premium domain that can't be replaced. The site makes you a lot of money. You bought a few links, have a few PBN links, but overall it's a site driven by whitehat links. In this case, paying someone to contact site owners, getting links removed, is worth the effort.
2. Your site is mainly driven by PBNs or paid links, the domain could easily be replaced by a new/different one. In this case, just get a backup of the old site, delete the old site, publish the same site/content on a new domain and start over again. Why? Because with mostly PBN/paid links, you'll only get the penalty removed by removing (almost) all of those links. You won't rank anywhere near the old positions because the reason for your rankings had to be removed to remove the penalty. Additionally, the chances to get penalized again while trying to regain the old rankings is high. Google forgives, but never forgets and if you are caught the second time, your chances of getting the domain out of the penalty are pretty bad. So, a fresh domain is the better choice.
301? Link based penalties usually jump over in a few days, so don't do it. You could get away with it for a few weeks, maybe even a few months if you are really lucky, but at the end 301s always transfer the good stuff and the bad stuff.
Edit: If you are going to pay for a penalty removal service (getting links removed, disavow, a nice reinclusion request template you can send to Google) never pay upfront. Getting manual actions removed is work, but if you know what you are doing and which (type of) links Google targets with those penalties, you can always guarantee success (success = penalty removed, not rankings returning to former positions!). May require a second attempt, worst case a third, but I'd never pay anyone without success because it means they don't really know what they are doing.
