If you are just trying to cash out a small sum of bitcoins with convenience and peace of mind as your utmost priority, then i would invite you to look into localbitcoins as a potential suitor. They are not really an exchange but rather an trading/advertising platform, but they can be used and considered as an exchange as well.
I have never had any problems with transacting on localbitcoins. Even if you get scammed you can recover your funds using their escrow system.
Obviously if you're cashing out a big amount, you're not going to use localbitcoins as your first choice because of the high spreads. But if your amounts are under 1 BTC then there is no problems at all. You'll get close to the amount you'll get on big exchanges like bitstamp.
I'm backing your Localbitcoins here too. If all you need to do is regularly cash out Bitcoin, then you don't want to do business with centralised exchanges (the ones you're looking at). As you can already see, they are all notoriously slow with Customer Support. If you have to use them, make sure all your accounts are fully verified (not just basic). It won't protect you from them locking your account when they feel like it, but they tend to be "nicer" to fully verified customers as I can see from my personal experience.
LBC is a p2p marketplace - so any reputable p2p would be perfect for you. You're selling to other people/traders like yourself, and as I've found trading only with reputable traders, transfers for selling my Bitcoin happen very quickly (Depending on the payment option or location). In at least two countries, I can sell and close the trade in 5 minutes, with instant online bank transfers. Plus I love the escrow.
You mentioned not an immodest sum, not to worry. The volume of Buy Orders on LBC is very good. If you don't like the spreads, set up your own Buy Order at around 1% better than market. You'll sell Bitcoins much slower that way, but if you're not in a rush, overall you get better rates than anywhere else.
Also, try Bisq. Similar p2p platform but with its own app and multisig escrow.