Below-grade and secured work areas tend to accumulate access controls for good reasons, and those controls have a way of becoming egress problems. Take the two issues separately.
The door. The rule is short: employees must be able to open an exit route door from the inside at all times without keys, tools, or special knowledge (29 CFR 1910.36(d)(1)). A device such as a panic bar that locks only from the outside is permitted. A door that releases only on a supervisor's command from a control room is the opposite arrangement; the fact that the supervisor is usually there does not help, because the requirement is at all times. Security needs are met by hardware that keeps people out while letting people out, not by hardware that does both.
How many exits. At least two exit routes must be available to permit prompt evacuation, located as far away from each other as practical so that if one is blocked by fire or smoke the other remains usable (29 CFR 1910.36(b)(1)). A single exit route is permitted only where the number of employees, the size of the building, its occupancy, or the arrangement of the workplace is such that all employees would be able to evacuate safely during an emergency (29 CFR 1910.36(b)(3)). That exception is a judgment about the space, and an area whose one exit depends on a remote release is a poor candidate for it.
The radiation work. No employer may use sources of ionizing radiation so as to cause an individual in a restricted area to receive, in any calendar quarter, a dose above the limits in Table G-18 (29 CFR 1910.1096(b)(1)). The employer must survey the radiation hazards (29 CFR 1910.1096(d)(1)) and must supply personnel monitoring equipment such as film badges or pocket dosimeters, and require its use, by each employee likely to receive more than 25 percent of the quarterly limit and by each employee who enters a high radiation area (29 CFR 1910.1096(d)(2)). High radiation areas must be posted and equipped with a control device or entry alarm (29 CFR 1910.1096(e)(3)). Any protective suit is selected through a documented hazard assessment (29 CFR 1910.132(d)) and does not stand in for monitoring.
The records. Employees and their designated representatives have a right of access to their own exposure and medical records, a right the standard says exists to improve the detection, treatment, and prevention of occupational disease (29 CFR 1910.1020(a)). When an employee asks, access must be provided in a reasonable time, place, and manner, and within fifteen working days (29 CFR 1910.1020(e)(1)(i)). Dose records that employees cannot see are a compliance problem before they are anything else.
In order of urgency: fix the door hardware today, evaluate whether a second route is required, and make sure the dosimetry and records programs are real. The first item costs the least and matters the most.