A few thoughts on a possible Danish intervention.
In OTL, Napoléon III was not averse to bringing Denmark into the conflict. At the 1866 peace negotiations in Prague between Austria and Prussia, it was the French emperor who insisted on the inclusion of the paragraph 5 stipulation, which opened for a possible plebiscite in Northern Schleswig (which would inadvertently have returned that part of the province to Denmark). As such there existed a considerable pro-French ‘faction’ within the Danish government.
Indeed, the army was actually mobilised in July 1870. Although it was a rather small force of 30.000 men organised into 31 infantry battalions (10 of those reservists), 15 cavalry squadrons (5 of those reservists), 12 artillery batteries (3 of those reservists) and 4 companies of engineers, it was envisioned as an offensively oriented field army whose primary function was to act in concert with the troops of an allied great power.
On the 5th of August, the French ambassador, the duke of Cadore, proposed just such an alliance and the prospect of a French expeditionary corps and naval units. Denmark, in return for her assistance, was to receive the whole of Schleswig. Although the king was vehemently opposed to the idea, a majority of the government’s ministers actually supported a French alliance (although they wanted to include the proviso that any - actual -fighting would have to be done by the French, whilst the Danes would act as mere “forces of occupation”....).
However, news on the 7th of August that the French had suffered initial defeats considerably cooled the heads of the otherwise rather revanchist Copenhagen opinion. Two days later, the government informed Cadore that it could not accept the French proposal on account of “... the imminent dangers such an alliance would bring upon Denmark.” Instead, the government eventually joined the general European league of neutrality in late August.
Now I’m not sure whether or not the French successes ITTL is enough to prevent the government of Ludvig Holstein-Holsteinborg (yup, that’s his name) from joining the league of neutrality. However, it’s a possibility for sure - although any actual military involvement would only be on the table after some darned spectacular French military victories.
Anyways, I hope this helps in some way
(Oh, by the way, killer timeline! Most def a fan right here!)