Reddit has some features that you can take advantage of to ease the transition. I'll highlight a couple that stick out in my mind as ones that would address your specific concerns:
User flair
You can enable "user flair" on a subreddit to allow users to assign images or custom text next to their usernames on post and comments. Here's an advanced example of user flair usage, by /r/SteamGameSwap to show steam profile URLs, an icon, and trade count on hover:

In a similar way, you can customize the look and feel of user flair however you'd like on your own subreddit. Some suggested use-cases:
- To establish aliases: set the user's old forum username as their user flair.
- To retain the forum's atmosphere: set an icon-sized thumbnail of the user's old forum avatar. You could aggregate these old avatars into a spritesheet and follow this tutorial to set them up on your subreddit.
- To reward users: Set special icons that are rewarded to community members as a benefit. You can add these to the spritesheet mentioned above.
User flair can be set up to be customizable by the user themselves, or only settable via the mods in the 'Community Settings' options. The level of customization you want to allow is up to you. You could spend some time searching through /r/csshelp to get an idea of other uses for flair as well.
Moderator Permissions
This won't totally solve your problem, but the top moderator of your subreddit can control the permission levels of the moderators below them. These permissions are available to moderators:
access - manage the lists of approved submitters and banned users. This permission is for the gatekeepers of the subreddit.
config - edit settings, sidebar, css, and images. This permission is for the designers.
flair - manage user flair, link flair, and flair templates.
mail - read and reply to moderator mail. By not granting this permission, you can invite third parties to manage your subreddit's presentation and flair without exposing private information in your modmail to them.
posts - use the approve, remove, spam, distinguish, and nsfw buttons. This permission covers the content moderation duties of being a moderator.
So former administrators could have full privileges, while former moderators may only have mail/posts permissions, designers may only have config permissions, and so on.
/r/modhelp has some further reading on moderator permissions, if you're interested.