Must an employer use the 190/month equivalnce set forth in 29 CFR 2530.200b-3(e)(1)(iv) for purposes of determining hours of service or can the employer adopt a different equivalnce if it is reasonable and accurate (such as 173 hours for each month of service)?

As far as I know, reasonable and accurate is not an issue when you are not counting hours & not using elapsed time. The equivalencies are the equivalencies, and the only exception is for a "shift" equivalency (DOL Reg. Section 2530.200b-3(e)(2)). Otherwise, when using an equivalency other than an "hours worked" y/s equivalency (DOL Reg. Section 2530.200b-3(d)), you must use one of the enumerated h/s equivalencies (daily, weekly, semi-monthly, or monthly).