Access Based Solution
A homegrown Access based solution that's somewhat difficult? You sir, are a gentleman and a scholar. Your discretion is to be applauded.
Your answer will be found in that Access solution. I promise this will make sense, stick with me. Access is a fantastic tool for people like me, for instance, who are only marginally competent at software development, but who know the intricacies of my company/division/role very well. Assuming there is someone similar in your clients organization who has worked on their internal solution, beginning your search in that internal solution is a good place to start.
You want to look for features/functions that seem weird, superfluous or just stupid, then find out why those features/functions were put in place. Are they addressing actual business rules and needs and/or organizational politics (both are equally important in the minds of clients) or are those features/functions the result of someone's best effort at conquering a technical challenge where a more appropriate answer was simply beyond their abilities. (For some reason, cascading drop down menus and variables of any sort seem to attract special sort of Rube Goldberg personality to all Access solutions).
Kooky technical workarounds can be safely ignored as long as you know what they are supposed to be doing. Just make sure any new solution handles that task in a 'proper' manner, and be certain to point it out to your client (just pointing out you felt their pain and solved it is worth 100 Client Bonus Points and if the opportunity to fluff the ego of whoever created the workarounds presents itself it's 1000 extra points. Especially if it's a middle manager person :).
The rest of it is down to simply assessing their homegrown solution and finding a 'shrink wrapped' alternative that meets their needs with the least amount of process change possible. Technical superiority, cost and ease of deployment (for you) aren't nearly as valuable as a smooth transition and a solution that actually works as opposed to turning off the building HVAC every time a calculated field returns a prime number (or whatever).
I'll close out with this; your job isn't to select their help desk solution. Your job is to figure out what their help desk solution actually needs to do. I guarantee they don't actually know. Selecting a product can be done by anyone who can read the features list. You've got to determine what they actually need, what they want and how they will determine if you were successful. Once you know those things it's a simple matter of you reading the features list and choosing the best fit and sending them a bill.
You've got a big advantage with them having an internal solution. Ask around and find the biggest pinch points for all the different users,and try to make them disappear in the actual deployment. It sounds kind of crappy, but try to identify who the heavyweight influences are in the user group, and which members of management are pushing for the new helpdesk and make sure you address their issues too. I realize users are actually the most crucial element, but the people who sign the checks are important too, and you can usually satisfy them with 3 seconds of attention and a chart with lots of primary colors.
But don't be shy about making a show out of listening to, and addressing what everybody wants from the end result. A solution is fit for purpose if it meets the clients ideas of the purpose, not its 'value added features' or technical superiority. The clients are telling you what they want, but they don't actually realize it, they never do. Listen to them and interpret it and if you do it well you can make lots of money. If you don't do it well you'll be another frustrated geek trying to get by in an illogical world, and nobody wants that :)
Also, for your own sanity, as you narrow down your field of contenders to a small(ish) set, start really digging into the documentation, help and support each solution has (user/admin documentation, not code comments & such). If you're going to stay in this field as a professional just accept the fact you won't get to charge for every phone call or support email if you want clients to do your marketing for you: You own those clients for all eternity. Make sure you can get answers if you need them. Besides, RTFM only works if there's a FM to read :)
I haven't done contract IT work in almost 14 years, and I still get occasional phone calls from old clients or their successors or recommendations from them to others. I would rather choke myself to death on slag from our blast furnace than do contract IT work again, but one day when you're old like me it'll be nice when you get those calls and can pass them off to some brave young person starting out and payback a favor to a former colleague or friend, and that's what makes the world go round.