I hadn't thought searching the internet would count as reinventing the wheel... Usually it is considered the easy approach. The options I mentioned above are the ones that most people here use to make money. Also, Barnes and Noble and Amazon are both free I believe for hosting Android apps. So you can use cocoonjs (premium - also free) or Intel Crosswalk to publish android games with for free. Creating an account for advertisements with admob, mopub, leadbolt, etc... are all free....
FGL allows you to upload for free, sponsors make offers to you on your game either for licenses or for ad revenue, most of the others do the same. Either gamejolt or mindjolt have a similar deal, I just forget which one... You can also look at MarketJS and many others. Most of these have come from this forum based on searches I have done. You may want to check the tutorials on adding the API's for Spil, FGL, etc... as they usually have folks that have used those services. One thing that pretty much all of them have in common as well is that they have standards and certain expectations so making money off a "crappy" game isn't exactly a viable strategy. Most of them will either want you to implement certain features, or be open to adding their advertising or branding to your game. Oh, another one you may want to check out is Kongregate. Also with facebook technically you could host on dropbox, at least until your game starts seeing a lot of play and then you would want to make sure you have a secure host. Currently I use hostgator and it is about $15 a month for their business plan which includes SSL.
If you look at the tutorial section and also at the export options in C2 you will get a good quick feel for some of the different marketplaces and portals that you can put your games on. Another important note is that you can't publish games for money unless you have a licensed version of C2 outside of publishing to Appbackr for tizen, etc... Hopefully if you can afford a license for construct, affording a hosting plan like hostgator or one of the other common cheap ones like bluehost, etc... shouldn't be a stretch. At the end of the day, most of the time you have to put a bit of money in to get any out. You will also find that sometimes making the game is easier than profiting from it.