The setting appears prettier in 1903!
Since the monument marked the site of the Famous Debate, when Lincoln posed the historic "Dilemma Question", that two-ton stone has not likely been moved very far.

Reading some of the material supplied by Fred G., I see that, the 6th Illinois N.G. Regiment was shipped from Springfield, Ill. to Camp Alger in Northern Virginia.

They bivouacked at Camp Alger, near Washington D.C., until being transported to Santiago, Cuba, and from there to Puerto Rico.
I would hazard to guess, the 6th Illinois N.G. was issued 'Trap-Door' Springfield rifles, at Camp Alger for the Cuba Campaign. When they embarked for Puerto Rico, they likely were issued Krag magazine rifles in Cuba.

I have a paper bond book on Camp Alger, which is an interesting read. Two of the Michigan Regiments, (33rd Mich. and 34th Mich.), also were sent to Camp Alger. They had a shorter stay in Virginia and got to Cuba in time to see some action.

This interesting book has references to the 6th Illinois N.G., but not, Co. L or Simon Ottenhausen specifically.

I have attached some content for everyone's enjoyment:

The 6th Mass. and 6th Illinois left Camp Alger on the same date, July 5, 1898, headed for Santiago, Cuba.

Arriving in Cuba, after the surrender of Santiago, both of these regiments were, subsequently, sent to invade Puerto Rico, likely re-equipped with Krag rifles.
(The land campaign in Puerto Rico lasted from July 25 to August 13, 1898, Ceasefire).

Attached pictures show a young 6th Mass. Soldier, (C.J. Duffy, Co. "C"), who went to Puerto Rico. He has a Krag, tropical uniform, and Spanish 'cockade' on his campaign hat.
(I saved this photo from off an ebay listing, a few years back).
A detail from a picture, (from "City of Canvass"), showing the 6th Mass leaving Camp Alger for Cuba with T-D Springfield rifles.
The Mass'. men seem to favor the 'Montana Peak' on their hats:

Wow!

I'm afraid BR may be right about the photo being mislabeled. By mistake or otherwise. But here is a photo of returning Spanish American War soldiers from Stephenson County Illinois, which Freeport is the county seat. Perhaps Simon Ottenhausen is in this photo.