Socal Pops, this is a great question and I have seen many families wrestle with this issue. For perspective, Div III schools make their offers near the end of the recruit's junior year in HS-- April/May of junior year. The "middle" prospects receive their offers later -- after the top prospects have turned down the coach. All of the Div. III coaches I spoke with wanted to have their recruiting class completed by end of summer after junior year. However, some Div III's can be super picky. For example, WashU is a fairly dominant wsoccer school in DIII (defending national champs) and they can take their sweet time and be really picky.
Let's say its June of Junior year. Coaches make your player offers. Coaches will not be happy if the kid takes their time "shopping " the offer etc. There will be pressure/indignation to commit. Once the player verbally commits to a coach, then the student/player will apply early decision in November of Senior year and is expected to accept the official, formal offer of admission when it arrives in December of Senior year.
However, a creative chess move/work around might be possible. Player can apply "Early Decision I" by November 1 to her first choice school. If she does not get in to her first choice then she would apply "Early Decision II" by January 1 to her second choice Div III school. Player can inform the coach of her second choice school of her plan to apply to them second even though she has an offer from them. Hope for the best. If your player is superior to what is on the DIII roster, then coach might be more open minded. Please note, not all schools have "Early Decision II" options.
But consider this: college rosters are gargantuan...30 kids, not 15-18 like in club... Playing time is no joke. If player "walks on" the coach has ZERO obligation to play him/her, unlike the "recruited" players who coach promised the moon to.
In conclusion may I suggest pursuing the Div. III offers so you have options...but by the time the offers roll in the choice will need to be made to play soccer or to go for the "dream academic school" w/out soccer. I am not able to envision a scenario where the player can aim for both unless your player would be vastly superior to what the Div. III coach has on their roster Please feel free to send message if you want more specifics. Congratulations to you and your player for looking ahead.