Are there different factors for access concentration depending on which jhana an individual is entering?

I can only answer first part of your question, i.e. if a meditator returns to access concentration between Jhana-states.

You are correct in that understanding. Here is a quote from the book "Practicing The Jhanas" by Tina Rasmussen and Stephen Snyder, which describes access concentration and that between entering the different Jhana-states the meditator returns to access concentration. Highlights in the quote are made by me:

ACCESS CONCENTRATION

Meditators can eventually attain access concentration using either type of momentary concentration practice—samatha or vipassanā. However, samatha practices are more likely to lead to access concentration because of their more stable nature. Access concentration is characterized by the significant reduction or complete dropping of the five hindrances and the arising and strengthening of the jhāna factors. For most people, a period of intensive practice is required to reach access concentration. In access concentration, the meditative experience becomes smoother, easier, and more pleasant because of this lessening of hindrances and the arising of the powerful and blissful sensations of the jhāna factors. This allows meditators to meditate longer and progress more easily in the practice.

It becomes a positive, self-reinforcing loop.It is easy to confuse momentary concentration with access concentration. One difference is that with access concentration, the meditator’s continuity with the object is much longer and more stable over time. Another difference is that with access concentration, the object is much more energized and “bright.”Most of the practices outlined in this book are samatha practices specifically designed to settle the mind and develop laserlike awareness, leading eventually to full absorption into the jhānas. Examples of samatha practices designed to develop access and absorption concentration are ānāpānasati meditation (as presented by the Venerable Pa Auk Sayadaw), the kasiṇas, thirty-two-body-parts meditation, skeleton meditation, and the bramavihāras (sublime abidings).

As access concentration develops, but prior to full absorption, it is also easy to confuse access with absorption concentration. In access concentration, the jhāna factors are present but insufficiently strong for full absorption into jhāna. (The differences between access and absorption are described below.) Even after a meditator has experienced full jhāna absorption and begins to move through the practice progression, access concentration continues to be used. With progression to each successive jhāna, the meditator first experiences access concentration as the awareness orients to the new experiences and increases in stability.

-- Practicing The Jhanas, p. 73-75

To make sure we're on the same page, terminology wise:

1. Factors - these are the factors or qualities of the various Samatha Jhanas - joy, well-being, equanimity etc.
2. Momentary Concentration (Kanika) - ability to stay focused on moment-by-moment arising and passing of phenomena.
3. Access Concentration (Upacara) - ability to stay focused on on a somewhat contrived stable object i.e. the breath, color, shape etc.
4. Absorption (Apana) - stable, one pointed mental state.

The Jhanas themselves are a continuum of mental states that don't exist as separate discrete entities. They are mental states that unfold depending on where in the continuum your experience lies. Somewhat like a rainbow - it is made up of different colors that have different qualities but on close examination they blend together seamlessly. The mind moves through these qualities in Jhana by focusing on the different qualities.

Generally speaking, deepening of access concentration increases the chances of the unfolding of Jhana. Once the first Jhana is established no special factors of access concentration are required to move into the second. The qualities of the first Jhana are :- pleasant sensations, joy, and sense of well-being. The meditation object of concentration (Samatha) is left behind and the minds merely abides (is absorbed in the Jhana qualities). When shifting through the Jhanas the focus just changes to subtler and subtler factors - from sensations to joy, from joy to well-being, from well-being to equanimity. So IMHO there is no dropping out of Jhana to gain access to next etc. or special factors of access concentration required. Five factors help to navigate the jhanas:

1. Directed attention (Vitakka) - directing the attention to a particular perception.
2. Sustained attention (Vicara) - sustain attention on an object.
3. Rapturous interest (Pita) - When vitakka and vicara are steady, a feeling of lightness and pleasure naturally occur.
4. Deep ease (Sukha) - Sukha is a quality of happiness that is much quieter and smoother than piti.
5. One-pointed attention (Ekaggata) - Ekaggata’s characteristic quality is to lock on to the chosen object with an intimacy that rivets the attention, stills the mind, and settles into unwavering focus.

These five elements of concentration — connecting, sustaining, rapture, joy, one-pointedness — take center stage during jhanic experience. Each level of absorption has its characteristic blend of these factors. Skill in entering and maneuvering through the levels of absorption depends upon cultivating these five factors. Catherine, Shaila. Focused and Fearless: A Meditator's Guide to States of Deep Joy, Calm, and Clarity (p. 108). Wisdom Publications.

Momentary concentration is cultivated specifically for vipassana practice but can result in Jhana as well. Daniel Ingram:

The vipassana jhanas differ from the concentration jhanas (samatha jhanas) in that they include the perception of the Three Characteristics, rather than the “pure” samatha jhanas that require ignoring the Three Characteristics to get them to appear stable and clean. However, the two may share many qualities, including very similar widths of attention and other aspects.