If he dies and the surrender is chaotic or looks suspicious, what would stop thousands of angry volunteers from taking to the hills and fighting incursions for another 5-15 years?
1) No one wants to be the last man to die in a losing cause. Most of the AoNV had only stayed as long as they did out of personal loyalty to Lee.
2) With Lee gone, most men’s highest loyalty was to their families, most of whom had written about fears of bandits, non-subservient blacks, and lack of food and clothing. They just want to go home.
3) Those hills were already full of Unionists who’d been resisting the Confederacy.
If they are having to garrison troops throughout the South, especially in parts of Alabama, Mississippi, the Carolinas, and Louisiana, then they will not have that many to spare for some foreign adventure that props up a quasi-friendly nation with claims on our southern frontier.
The Union garrisoned troops throughout the South for a decade in OTL and was easily able to move a spare 50,000 to the Texas border in OTL. Should France not back down, the Union will not demobilize. A lot of former Confederates would probably become galvanized Yankees for better food, clothing, shelter, and pay than the got in the Confederate Army.
Guatemala is a state on the verge of implosion in 1870 with conditions similar to Mexico in 1864 with haciendas employing serfs/slaves, the church and cabal of landowners running everything, and a secession crisis already brewing. If their northern neighbor and former master Mexico can do it while allowing the Guatemalans some level of autonomy, I think it's a strong possibility they move to a strong Mexico that can provide order and stability.
How often does an independent state voluntarily join an empire? I can think of a handful of examples where independent states voluntarily joined a republic, but empires expand by conquest. Speaking of empires, the British in British Honduras will probably not like Mexico expanding southward.
Expecting they would get any degree of autonomy would require a significant level of naïveté on the part of Guatemalan leaders Mexico offering it to Guatemala risks other parts of the Mexican Empire demanding more autonomy. The most likely area to do this is the Yucatan.
Voluntarily joining Mexico runs counter to Guatemala’s behavior throughout the 19th Century. Guatemala seceded from Mexico as part of the Federal Republic of Central America in 1823 and left that in 1840. They were the first to leave the 1842 attempt to restore the Federal Republic of Central America. They did not join the Federation of Central America in 1852 nor the Greater Republic of Central America in 1896.
El Salvador, Honduras, and Nicaragua join within the following 15 years and Mexico profits greatly from the Canal along its southern border.
Mexico could probably conquer these states, but like Guatemala they would not voluntarily join the Mexican Empire. Mexico might get enough investors in a Nicaraguan Canal after de Lesseps fails in Panama, but that does not guarantee successful completion, let alone a profit. Best case, Mexico completes their canal around 1900. Your plan for paying off the investors and exempting Mexican ships from tolls means the Mexican government probably has to wait another decade or two before they start getting a taste of the profits.
Costa Rica prefers a master who speaks its own language and who helps them build the railway between Puerto Limon, San Jose, and Mexico City by 1888 (in OTL an American businessman did this).
Costa Rica was the most independence minded of the Central American states. After the collapse of the Federal Republic of Central America in 1840, they did not join the 1842 attempt to restore it, nor the Federation of Central America (1852), nor the Greater Republic of Central America (1896-98), nor the second Federation of Central America (1921-22)
Panama remains in the hands of Colombia until 1890 when Mexican "assistance" liberates the nation as a satellite and buffer state.
Seizing Panama while the French are still building their canal will have a strong possibility of triggering armed response from France and perhaps Britain and the US as well.
Mexico might even be able to snag or buy a few Caribbean possessions from a desperate UK during WWI and help Cuba gain independence from Spain
This is reminding me more and more of your bog-standard Confederacy-wank with Mexico substituted for the Confederacy. It requires effortless assimilation of minor powers, major powers never doing anything to get in the way, perfect internal harmony, unprecedented growth of industry and the economy, and nothing ever going the slightest bit wrong.