Can you please show a image with the blue you mention inside the bottom bracket? The paint on the bearing cups is of no use. Is there any paint inside the head tube? When you hit the last blue color was there a primer coat as the base?
One must wonder about the stamping on the top of the bottom bracket. We have seen such stampings performed by local police departments on other bicycles. Would someone take a 1928 bike to a police station when it was 7 years old to be stamped? Possibly those stamps were done by a bike shop when the bike went in for an overhaul? You would thing a someone who refurbished the bike would have done a better job stamping and would have put them on the underside to be more discrete. My opinion is the top stamping was performed by a police station because it is so messy.
As Matt said above for the bike to be a 1928 model it would have the post 1923 Indian badge. With the later badge we really do not know how long Indian used that badge. There are a couple late 30's balloon tire Indian known with this "Indian Motocycle Co" badge. I personally own a Columbia made lightweight (it is heavy as hell) sports tourist model with this said badge. The problem is literature for the Indian bicycles during the 30's and early 40's is very scant. I have just learned of a circa 1940 +/- Indian/Columbia catalog that exists but have yet to see it (this piece of literature may be helpful to you because according to the previous owner of this catalog Indian offered many different models). There is not a single piece of
Indian literature currently known that shows the 1936/37 German made balloon tire model.
The seller added your badge to that bike so it needs to be completely disregarded. This brings up another issue with the Indian badges. The "Hendee" badge you have has holes that are horizontal or nearly horizontal. The post 1923 badges I am aware of the holes are greatly offset. As mentioned above, we do not know how long this badge was used but it seems to be approx. 20 years (off and on). I do not claim to be an expert on the badges; maybe some of the "Indian Motocycle" script badges have a more horizontal orientation to their mounting holes? Hopefully a badge collector or expert can chime in here. A final question related to the badge; when you striped off the paint did you find any other holes on the headtube?
The fact the bike seems to be Westfield build and you have a classic Indian chain ring is positive. I don't think anyone has seriously done much research to determine what bicycles Indian was offering in the late 20's & 1930's; a good start would be at the museum in Springfield. The second place to look would be their monthly magazine published in the period that presumably from time to time show Indian's bicycle offerings. We have yet to see a single piece of this literature this is a great opportunity.
If I owned your bicycle I would be trying to research to determine the mounting holes vary on the the later badges. I would also try to find the 1928 (into the 1930's) monthly magazine and any dealer catalogs with the full offerings to determine what bikes were offered and when. Good luck with your quest.
Here is the badge the bike should have if it was 1928 or from the 30's:
This is the best loose Indian badge I have ever seen. With OG nickel and painted details in excellent condition. Display case included. Please PM to purchase. Provenance: Ex. Mel Short Collection
thecabe.com