After the British Empire ended slavery, the apprenticeship system was set up as a de facto form of slavery. What if another solution to compensate slaveowners was done: the British Government buys up slaves to fight in the imperial armed forces? How feasible is this?
Not very.
A) Because the idea of arming blacks en masse would cause large sections of the populace to freak out
A large section of the British army was formed from those who joined because they were desperate - i.e. that a life in the line of battle was seen as an improvement for them. Either they were destitute, or on the run from the law, or the law itself had given them a choice between soldier, sailor or scaffold and they didn't want to be executed or pressganged. The army suffered scores of desertions but a lot of the soldiers were willing to remain because it was the only option they had, save trying to defect to the country where they were the enemy without even knowing a word of the language. Selling slaves into the army gives them freedom and a wage yes, which would be a massive improvement on their expectation of a life of enforced and unpaid labour, but I suspect a large number of slaves would see a life in the army being paid to be fired at thousands of times to be no better. Difference is, ironically, the army is much easier to flee from, owing largely to its very mobile nature, and the way that the soldiers themselves are the ones preventing each other from leaving. You just wait your turn on picket duty, and then run. No-one's going to catch you because you're the one supposed to be catching you. For a huge financial outlay involved in buying the slaves to work the army and then paying them to boot, the army would become awash with desertions, and understrength battalions are going to really suck in battle.
To repeat - google West India regiment. They had an outstanding service record and desertion was no greater a problem than for any other units.
BTW, I don't know what your definition of "en masse" is, but the active strength of the West India regiment peaked at something like 17,000 men towards the end of the war, and that's of course ignoring how big the also noticeably dark skinned Indian army got on occasion.
I remember reading several books that said that the British did sign up slaves to fight in their army during the American Revolution. Here is an excerpt from Wiki on Lord Dumore Proclamation.
Lord Dunmore's Proclamation
Dunmore is noted for Lord Dunmore's Proclamation, also known as Lord Dunmore's Offer of Emancipation, on 7 November 1775, whereby he offered freedom to slaves who abandoned their Patriot masters to join the British. This was the first mass emancipation of slaves in North America. As governor of Virginia, Dunmore had withheld his signature from a bill against the slave trade.[2] However, by the end of the war, an estimated 100,000 escaped slaves sought refuge with the British, an estimated 20,000 of them served in the army, though the majority served in noncombatant roles.
He organised these Black Loyalists into the Ethiopian Regiment. However, after the Battle of Kemp's Landing, Dunmore became over-confident, which precipitated his defeat at the Battle of Great Bridge, 9 December 1775. Following the defeat at Great Bridge, he loaded his troops, and many Virginia Loyalists, onto British ships; as there was an outbreak of smallpox at the time, this had disastrous consequences, particularly for the ex-slaves; some 500 of the 800 members of the Ethiopian Regiment died.
Difference is, these black units were all volunteers. The OP suggests that slaves were being bought to join the army - i.e. they were being forced into it in the same way that plantation slaves were forced to work the plantation fields.