I actually disagree from a non-RP as well as an RP perspective.
Imperial Slavery is more of a form of Indentured Servitude, as you've demonstrated you agree with. But something people always conveniently forget is very simply this: Morals are purely subjective to the time, place, and people. Now, let's go ahead and take a look at what Imperial Slavery really is.
An Imperial Citizen, who is under such a crippling amount of debt to even consider it (this is VERY important, we aren't talking about a semester's worth of student loans, we are talking the kind of debt that leads people to file Chapter 13 (complete and total, non-recoverable bankruptcy for non-US readers) at best case scenario, and wrap their lips around the barrel of a loaded gun worst case) decides to sell themselves into slavery for a set number of years. These citizens have no recourse available to them. Now, how does our current economy, as well as the Federation handle this? The most simplified version is nothing. The person spends the rest of their life in a state of perpetual debt, often times either scraping to survive, being pushed to illegal activity to attempt to settle the dept, or, as stated, some choose to end their own life seeing no escape and no improvement to their situation coming. Ever.
Now let's take a look at Indentured Servitude, or Imperial Slavery. First and foremost, the lore established that Imperial Slaves are not treated as animals or property save the simple definition of "I own this person". They are fed, watered, given housing, and unlike modern slavery, treated with respect and honor. This is built into the tenants of being an Imperial citizen. You behave honorably. This includes how you treat your slaves. There is no honor in beating your slaves, or belittling them. The flip is also reverse though, this Slave knows why he's in the situation. There is no honor in running away without settling your debt, there is no honor in refusing to do your duties. I don't believe the lore establishes length of servitude, but I know that life-spans in the 31st century are much longer than now. This means that 20-30 years of indentured servitude is nothing to clear yourself of all debt.
Now, the lore also establishes another custom to be aware of, and take into account when determining your moral stance: Many times, Slaves are provided with essentials by their "owner" upon leaving, for some corporations, this includes an option to stay on with pay, sometimes the slave is given a house, or a ship, or any other number of basics to start them off. The Empire has a clear and divided caste system, unlike the vague "lower" "middle" and "upper" class titles given to citizens of the US, Europe, and other modern countries. Most slaves who serve their terms honorably (which is a wide majority) exit their terms at a higher cast rank then when they enter. This is an improvement.
To me, this is an elegant and safe solution for what to do with debt. Someone buys your debt, pays it off, then, you work for them for x years until you're settled, getting a fresh lease on life in the process. Then there's that other simple concept that many people don't like: We have no rights.
Intrinsically, and very simply, humanity is no more special than that fly you just killed absentmindedly while reading this post. We have a set number of trips around our local star, which is not even a pimple on the butt of the photo-plankton of the ocean that is the known universe. We're each individually less than an atom of the that makes up that pimple on the plankton's butt. We tell ourselves that we have certain rights, and that we are owed something, but if you step back, and look at it objectively, these "rights" are just something our society determined was important. It is not a law of the Universe.
If a human goes their entire lives without freedom, without being able to shape their own destiny, what recourse does the Universe have? None. Zip. Zilch. Nada. Cero. Nul.
If someone tries to go faster than light, what happens? The Universe Slows Down Time to keep them from doing so. Imperial Slavery takes a serious problem and gives it an, in my opinion, elegant solution, given the variables provided. Were similar variables present on present day Earth (namely the longer life-span and in-built value of behaving in a specific manner towards "slaves") I'd dare-say I'd even be for it myself.