If Web Services doesn't have any options for Checkbooks, there isn't any setting or configuration, by default, that adds more functionality, it pretty much is what it is and has been that way since we changed Web Services back in GP 10.0 and that was just to move it from IIS to WCF.
Usually, if Web Services and/or Integration Manager doesn't have the functionality being looked for, such as Checkbooks, the default is eConnect as that does have, in most cases, the procedures to do what you're looking to do, and if it doesn't, a PRE or POST procedure can possibly be modified to do what you need it to do. You can call the eConnect API directly.
Another option may be Visual Studio Tools, using .NET languages to build an integration add-in for Dynamics GP.
Understanding you are unable to use econnect in your environment, I would leave this to the forums community to see if there is someone that has and/or knows a customer in a similar environment and what they may be using in a situation like yours, to provide more in-depth information.
Thanks