What you've described is a typical, standard business and marketing question.
Realistically, if a business user base is not motivated to purchase an application, it's probably not full of features they require. You might think it's a great application, and it may be, but what really matters to a business like you're managing with this application is what the consumers want.
Ask them.
What you require is marketing research, and then allow the results of that research reshape your application design, so it provides enough of the features they demand that they'll pay for it.
At which point a free version is no longer required, but if you still use that approach, you would then expect sufficient user base to make advertising sufficient to produce income, or at least lead to paid users for whatever reason motivates them (fuller feature set, remove the advertising, etc.).
What will not succeed is to make an application without marketing research and then try to fashion a way to sell it as it is - unless it just HAPPENS to be something highly desired.
Put another way, you're contemplating if a free version would generate attention. It may, but it may not generate the attention you desire. It may give everyone a chance to discover they don't want it as it is, but would if it did something else. That could be marketing research - feedback, which then motivates new development - becomes a cycle of responsiveness business users require.
I read a blog about 8 months ago lamenting the development of an Android game. The fact it was a game is of no consequence, really - business is similar no matter what you're selling. The point here is that the author created a product, made perhaps $1,600 over several months and was seriously disappointed - it took 6 months to create the product, and the author earned pennies on the hour.
The problem was multifaceted. The product was typical, perhaps mediocre. It wasn't marketed - it was simply put on the store and left there to attract purchasers. There was no buzz, there was no awareness in the public, and it didn't do something which demanded attention of the consumer base, making it attractive enough to sell.
The author concluded that application development on Android was a loosing game. With that approach, it is. No matter what one thinks about selling applications on the store, it's a business. One must understand the basic concepts of business, of sales, of marketing, of advertising and of research in order to make money doing it.