Managing the lifetimes of garbage-collected objects

I am making a simplistic mark-and-compact garbage collector. Without going too much into details, the API it exposes is like this:

/// Describes the internal structure of a managed object.
pub struct Tag { ... }

/// An unmanaged pointer to a managed object.
pub type Pointer = *mut usize;

/// Mapping from old to new locations.
pub type Adjust = BTreeMap<usize, Pointer>;

/// Mark this object and anything it points to as non-garbage.
pub unsafe fn survive(ptr: Pointer);

pub struct Heap { ... }

impl Heap {
    pub fn new() -> Heap;
    
    // Allocate an object with the specified structure.
    pub fn allocate(&mut self, tag: Tag) -> Pointer;
    
    /// Move all live objects from `heap` into `self`.
    pub unsafe fn reallocate(&mut self, heap: Heap) -> Adjust;
}

This API is obviously fundamentally unsafe. I would like to rework the API (without changing the internals, which are just fine!) to account for the following facts:

1. All Pointers to (objects allocated in) a Heap become invalid when the heap is merged into another heap.

2. merge returns an Adjust whose values are valid Pointers to (objects allocated in) self.

I have the following tentative solution:

// Replaces Pointer.
#[derive(Copy, Clone)]
pub struct Object<'a> {
    ptr: *mut AtomicUsize,
    mark: PhantomData<&'a usize>
}

impl<'a> Object<'a> {
    pub fn survive(self); // Now supposed to be perfectly safe!
}

pub type Adjust<'a> = BTreeMap<usize, Object<'a>>;

pub struct Heap { ... }
pub struct Allocator<'a> { ... }

impl Heap {
    fn allocator(&'a self) -> Allocator<'a>;
    // The following doesn't work:
    // 
    //  fn allocate(&'a mut self) -> Object<'a>;
    //  fn reallocate(&'a mut self, heap: Heap) -> Adjust<'a>;
    // 
    // Because it doesn't allow the user to allocate more
    // than one `Object` at a time (!) in a `Heap`.
}

impl<'a> Allocator<'a> {
    // Note that the resulting `Object`s are tied to the `Heap`,
    // but not to the allocator itself.
    fn allocate(&mut self, tag: Tag) -> Object<'a>;
    fn reallocate(&mut self, heap: Heap) -> Adjust<'a>;
}

Is this design correct? If not, what needs to be changed?