Step back and take a look at your problem from a different viewpoint. What is the worst thing that could happen if you used sequential numbers? You've mentioned enumeration: what is the threat from enumeration? Can someone cause a problem if they see you issue #00015 and #00016, and predict that ID #00017 will likely be generated next? Perhaps someone could hijack an email or twitter account that will likely be associated with an upcoming ID.
And what is the problem if someone can determine that ID #00023 is older than ID #42234? Do older IDs generally have more resources available than newer IDs? Perhaps I know that ID #00123 was issued on May 1st, and ID #00256 was issued on June 1st; if I learn that some popular celebrity announced they signed up in May, I have only 133 numbers to guess their ID. Does guessing someone's ID# cause anyone a problem, or is it going to be public information anyway?
At this point you should understand if sequential ID #s truly have to be kept secret, or if they can be public.
Then take a look at the threat vectors, (if these are realistic threats,) and come up with the risks. Most of these appear to be risks to your clients if their secret IDs become public, and less of a threat to your systems. But if you aren't protecting your clients, your reputation will certainly be destroyed, and your venture will fail. So if these are valid threats, you have to take them seriously.
Next, add in the understanding that a Pseudo-Random Number Generator (PRNG) was created for exactly one specific purpose: generating statistically well-distributed numbers for modeling problems in statistics. They were never created to generate "unguessable" numbers. Most PRNGs are only a math problem away from being a sequential number generator. You can try jumping through many seeding hoops to reduce the ability to generate guessable numbers, but that's exactly the problem a Cryptographically Secure PRNG (CSPRNG) is designed to solve. CSPRNGs were specifically designed to generate unguessable numbers.
Now that you better understand some of the risks, you should appreciate why you need (or don't need) to protect your clients from these threats; and with a better understanding of the differences between a PRNG and a CSPRNG, you can arrive at a solid decision.
If you have to keep these secret, then you must use a CSPRNG to protect your clients. If you don't need to keep them secret, then you should use a sequential number and reduce the complexity of your system by eliminating the random number generator altogether.