I know some older boats had a cast "wing" type eye. That would work nicely with yours.
The issue I see (from your pic) is the angle of the prow. It looks like a very sharp angle in the prow. A drill through is going to be difficult to get proper support for the nuts from behind.
What you may have to do is file a "shim" to make a level backing surface (ie: file a beveled filler piece so it sits into the back of the stem) so you can tighten down the nuts without deforming the prow/stem. It will also help to spread the load over a larger surface when loading and during road travel, thus lessen the chances of developing a crack over time.
The bow eye should be below and up against the bow stop in order to secure the boat from sliding forward and up on the trailer when stopping. The loading winch should be mostly a straight forward pull to load the bow eye into the stop/roller.
While its not as critical on a tinny, a safety buckle/chain from the eye to the trailer frame is also a good idea. It helps to restrain the boat from forward motion in an accident or emergency stop and can restrain the boat should your winch ever have the locking pawl slip or pop open.
I'm currently in the process of rebuilding my dads old tinny and trailer so it all fits properly:
You can see here how the winch used to pull it down:
At first thought that's not a bad idea, but it loads the keel against the center roller and thats not so good for stressing the hull when road moving. It also makes it more difficult to pull the boat tight up against the stop. Straight pull is much better.
My inherited old tinny is a sprinbok (princecraft) ungava. The bow eye on this boat is just a formed piece of aluminum and two bolts retaining it:
That's as delivered from the factory. Not the best pic, but you can see it if you zoom in.
Additionally, your transom should be supported by the bunks. The bunks should extend a few inches behind the transom.
Lastly, you should balance the weight and get the tongue loading right so you don't get a tail wagger. Load on a tinny isn't usually a problem as the trailer often weighs more than or the same as the boat, but you should have 7-10% of the gross trailer weight on the tongue to tow comfortably without "wag"...
Its all kind of a balancing act to get it all right. Sliding the winch post back and forth, bunk lengths, axle positions, etc. You just have to keep tweaking and adjusting until you get there.
Tinnys are pretty forgiving towing for the most part, mostly down to the low weights involved.
This all sounds like a lot, but it's mostly just time. The only cost involved is for a bow eye, a small chunk of aluminum block and a length of chain/strap if you want to add a safety chain/strap to the bow. The rest is just adjusting what you already have....
Cheers.