Ok so you have two avenues here and people focus usually on one and not the other.
I'm a local dentist and struggled with the map pack. I find it easy to rank number one for terms with a local identifier like 'product+location' which always trigger the maps.
The problems you might encounter are that the maps are great but they take the user to the home page. This is problematic because I'd actually rather them be taken directly to my product page and not have to navigate around to find what they're looking for. So maps are great but they do have this annoying limitation in UX and I find from looking at user feedback from recordings (like from Hotjar) that they can get lost and pogo back to the serp - always bad.
The other limitation is NAP-W. So it can be worth getting your NAP absolutely squared away - which it sounds like you have. But I got some great results from doing an audit with a company called whitespark who basically do it for you for a few hundred dollars. Moz also have a great tool but it's not working here in the UK at the moment. However, my NAP was in a mess so you may well not need these although it's a small investment and got us from 7% to 14% in the maps (out of thousands of positions) so that's a LOT of map 1-3 positions.
So places you must go are:
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INDUSTRY SPECIFIC (like universities and local clubs and trading links with local businesses and local bloggers) Bloggers want money and for hardly anythign they will publish nice advertorial that will move the needle.
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LOCAL - It has to be local. google 'Hyper local citations' for some examples.
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BUSINESS - and this is the one people neglect. You sell a product but you are also a business so get in touch with local business groups, start up organisations and write articles about business. Then you have two sources of links. Your product and general business stuff too. This is how I've had some massive successes. Local newspapers will write about small businesses and the people and stories behind them. Use this.
Avoid signing up to rubbish local directories. They don't work. I read in Search Engine Roundtable - (which is reputable) that there are still some good directories out there but I ran them through my systems and they are all absolute rubbish. I respected that company and really lost a lot of respect for them when they were touting these crappy listing companies. Probably paid. Who knows.
Remember NAP and directories are different. You need to be listed in relevant citation sources like local newspaper directories for businesses but the old web directories are a waste of your time and money.
If you have professionals working in any of your client organisations get them to write for their university alumni - if they went to uni in their city this will skyrocket your local pack presence.
But if you are new it can just take time. So be patient and don't try anything shady to try to game the system. Google is getting smarter and smarter and what worked even 6 months ago will get you penalised after the huge quality and link algo changes that happened in March, April and possibly in May too (of this year)
Also remember link building cannot be done without building relationships with real people. It's essentially now PR. Doing real things with real people in the real world. Gone are the days of basement linkbuilding. Use your brain not the tools. And don't copy other sites because what they did 9 months ago might now be banned in the eyes of google. Sure model their successes but don't blindly follow their strategies - they might be working with less reputable agencies and you'll do yourself harm.