Circling back on this just in case anyone else experiences a similar frustration when trying to port a custom password complexity solution developed on v7 over to v8. Ultimately, the problems we faced which required custom development were:

1. Capturing the date/time the last time a user logged in (Note: this snippet is redundant as you should be able to rely on the lastLoginDate column in the umbracoUser instead of capturing this data elsewhere.)
2. Storing the user's last 6 passwords
3. Ensuring the user's new password is not the same as their last 6 passwords
4. Ensuring the user is not attempting to change their password within 24 hours of last changing their password

All of the other complexity requirements were handled via the default properties of the default UsersMembershipProvider.

The final solution ended up being to replace the custom Umbraco membership provider with a custom BackofficeUserManager. Then, create a startup class that is derived from the UmbracoDefaultOwinStartup that configures your services. Finally, update the owin:appStartup appsetting in the web app's web.config after you've added the reference to the custom DLL. See below for the full manager:

using Client.Umbraco.v8.Security.Factories;
using Microsoft.AspNet.Identity;
using Microsoft.AspNet.Identity.Owin;
using System.Collections.Generic;
using System.Threading.Tasks;
using Umbraco.Core.Configuration.UmbracoSettings;
using Umbraco.Core.Models.Identity;
using Umbraco.Core.Security;
using Umbraco.Web.Security;

namespace Client.Umbraco.v8.Security.Managers
{
    public class ClientBackOfficeUserManager : BackOfficeUserManager
    {
        public ClientBackOfficeUserManager(IUserStore<BackOfficeIdentityUser, int> store, IdentityFactoryOptions<BackOfficeUserManager> options, 
            MembershipProviderBase membershipProvider, IContentSection contentSectionConfig) 
            : base(store, options, membershipProvider, contentSectionConfig) { }

        #region Protected Override Methods

        // Invoked each time a user logs in
        protected override void OnLoginSuccess(IdentityAuditEventArgs e)
        {
            int userId = e.AffectedUser;
            var service = PasswordServiceFactory.Create();
            service.SetLastLogin(userId);

            base.OnLoginSuccess(e);
        }

        // Invoked each time a user changes their password, including on reset
        protected override async Task<IdentityResult> UpdatePassword(IUserPasswordStore<BackOfficeIdentityUser, int> passwordStore, BackOfficeIdentityUser user, string newPassword)
        {
            var service = PasswordServiceFactory.Create();
            // Ensure password is not the same as the last 6 passwords
            var validPassword = service.CheckPasswordDuplicates(user.UserName, newPassword);
            // Ensure password meets age requirements
            var ofAge = service.CheckPasswordMinimumAge(user.UserName);

            List<string> result = new List<string>();

            // Obfuscate error message to prevent exposing business rules to potentially malicious parties
            if (!validPassword || !ofAge)
            {
                result.Add("Password reset failed. Please try again later or contact your System Administrator if you continue to have issues.");
            }

            if (result.Count != 0)
            {
                // Note: error messages displayed on password reset, but not on set
                return IdentityResult.Failed(string.Join(" ", (IEnumerable<string>)result));
            }

            // Let Umbraco validate and store the new password
            var updatePassword =  await base.UpdatePassword(passwordStore, user, newPassword);

            if (updatePassword.Succeeded)
            {
                // Capture updated password on success
                service.SetPasswordHistory(user.Id, newPassword);
            }

            return updatePassword;
        }

        #endregion
    }
}

We also leveraged this fantastic project from Sebastiaan Janssen to supplement the removal of the scheduled tasks from v7. Not only were we able to create tasks to disable users who hadn't logged in in over 150 days, we can send users who haven't changed their passwords in 90 days a reminder about their password expiring as well as programmatically resetting their passwords if they fail to change it before that time runs out. It also comes with a sweet UI in the dashboard where you can see the task results, run them manually, etc.! I highly recommend that project for all scheduling needs and kudos to Sebastiaan for working on Umbraco, even when he's not at HQ.